Nohutu haşladıktan sonra birazını salataya koydum, birazını da mercimek yemeğinin yanına ayırdım.

Because nohut is the direct object of haşlamak in the clause nohutu haşladıktan sonra.

The ending -u here is the definite accusative. Turkish often uses the accusative when the object is specific or already identifiable.

• nohut = chickpeas / chickpea
• nohutu = the chickpeas / the chickpea, as a specific object

So:

• nohut haşlamak can sound more general, like to boil chickpeas
• nohutu haşlamak means to boil the chickpeas / boil that chickpea ingredient

In recipes and everyday speech, Turkish often treats ingredients as specific items being worked with, so the accusative is very natural here.

-dıktan sonra means after doing ....

It is attached to a verb stem to create a time expression:

• haşla- = boil
• haşladıktan sonra = after boiling

So:

• nohutu haşladıktan sonra = after boiling the chickpeas

This structure is extremely common in Turkish:

• yemek yedikten sonra = after eating
• eve geldikten sonra = after coming home
• bitirdikten sonra = after finishing

It is basically a subordinating structure: one action happens, and then the main action follows.

Birazını means some of it rather than just some / a little.

That extra ending shows that we are talking about a part of something already mentioned. In this sentence, the thing already mentioned is nohut.

So:

• biraz = some, a little
• birazını = some of it

The form contains:

• biraz
• a possessive-type element that helps make it refer back to a known whole
• the accusative ending, because it is the object of koydum or ayırdım

This is a very common pattern in Turkish for partitive meaning:

• ekmeğin birazını yedim = I ate some of the bread
• suyun birazını içtim = I drank some of the water

In your sentence, birazını ... koydum, birazını da ... ayırdım means I put some of it in the salad, and I set some of it aside ...

Because the speaker is dividing the chickpeas into two portions.

The structure is:

• birazını salataya koydum
• birazını da mercimek yemeğinin yanına ayırdım

This literally means:

• I put some of it in the salad
• and I set some of it aside for/next to the lentil dish

Repeating birazını makes the distribution clear: one portion went one place, another portion went elsewhere.

This is a very natural Turkish way to express splitting something up.

Because koymak often takes the place something is put into / onto / to in the dative case.

• salata = salad
• salataya = into the salad / to the salad

So:

• salataya koydum = I put it in the salad

This is similar to many Turkish motion-or-placement patterns, where the destination gets the dative:

• masaya koydum = I put it on the table
• çantaya attım = I threw it into the bag
• dolaba yerleştirdim = I placed it in the cupboard

English uses prepositions like in, into, on, but Turkish often uses the dative plus the verb to express that idea.

Here da means something like too, also, or and as for another part.

It links the second action to the first one:

• birazını salataya koydum
• birazını da ... ayırdım

So the sense is:

• I put some of it in the salad, and I set some of it aside as well ...

In this sentence, da helps show that the second birazını is an additional portion.

Important: this da is the separate word meaning also/too, not the locative case ending -da/-de.

Compare:

• Ben de geldim. = I came too.
• Evde kaldım. = I stayed at home.

Because yanına adds the meaning to the side of / to accompany.

• mercimek yemeğine ayırdım would suggest I set it aside for the lentil dish
• mercimek yemeğinin yanına ayırdım more specifically means I set it aside to go alongside the lentil dish

This is very natural when talking about food served as a side.

Breaking it down:

• mercimek yemeği = lentil dish / lentil stew
• mercimek yemeğinin = of the lentil dish
• yanına = to its side / alongside it

So the full phrase means:

• to the side of the lentil dish
• more naturally in English, to have with the lentil dish

Because yan is a relational noun meaning side, and relational nouns in Turkish usually appear in a possessed structure.

So yanı means its side, and the thing it belongs to takes the genitive:

• evin yanı = the side of the house
• masanın yanı = the side of the table
• mercimek yemeğinin yanı = the side of the lentil dish

Then with dative:

• mercimek yemeğinin yanına = to the side of the lentil dish

This is a common Turkish structure. English often uses a preposition, but Turkish often builds the relationship with a genitive + possessed noun pattern.

Ayırmak basically means to separate, to set apart, or to reserve/set aside.

In this sentence, it means:

• I set some aside

Because it is followed by mercimek yemeğinin yanına, the full meaning is something like:

• I set some aside to serve with the lentil dish

So it is not just physical separation in an abstract sense. In food context, ayırmak often means reserve a portion for later or for a particular use.

Examples:

• Birazını çocuklar için ayırdım. = I set some aside for the children.
• Yarına biraz yemek ayırdım. = I saved some food for tomorrow.

Yes, it appears in the singular form, but in Turkish that does not necessarily mean only one chickpea.

Turkish often uses the singular form for:

• ingredients
• mass-like food items
• generic substances or categories

So nohutu haşladım can naturally mean I boiled the chickpeas.

This is similar to how Turkish can say:

• patates doğradım = I chopped potatoes
• fasulye pişirdim = I cooked beans
• mercimek aldım = I bought lentils

Even though English often prefers plurals like chickpeas or beans, Turkish frequently uses the base singular noun for the ingredient as a whole.

Because the verb ending already shows the subject.

• koydum = I put
• ayırdım = I set aside

The ending -dum / -dım marks first person singular: I.

Turkish usually leaves out subject pronouns unless they are needed for emphasis or contrast.

So:

• Ben koydum = I put it with extra emphasis on I
• koydum = simply I put it

That is why the sentence sounds natural without ben.

Because Turkish is generally a verb-final language.

The usual pattern is that:

• time expressions
• objects
• destination phrases come before the verb

So in this sentence:

• Nohutu haşladıktan sonra = after boiling the chickpeas
• birazını salataya = some of it into the salad
• koydum = I put

Then:

• birazını da mercimek yemeğinin yanına = some of it too to the side of the lentil dish
• ayırdım = I set aside

For English speakers, this can feel backward at first, but it is completely normal in Turkish.

Yes. That is exactly what is happening.

Once nohut has been introduced, Turkish can refer back to it with birazını = some of it.

So the structure is:

1. mention the whole: nohutu
2. refer to parts of that whole: birazını ... birazını da ...

This is very natural Turkish discourse structure. English does the same kind of thing:

• After boiling the chickpeas, I put some in the salad and set some aside ...

Turkish simply marks that some of it idea more explicitly through the form birazını.

Yes: it sounds very natural and everyday, especially in a cooking or meal-preparation context.

A few things contribute to that natural feel:

• haşladıktan sonra gives a clear cooking sequence
• birazını ... birazını da ... neatly divides the ingredient into portions
• mercimek yemeğinin yanına sounds like ordinary meal planning: one food is being prepared as a side for another

So this is a good example of practical, idiomatic Turkish rather than textbook-only Turkish. It reflects how Turkish speakers often talk about preparing food step by step.