Havuçları küçük küçük doğradıktan sonra mercimeğin içine ekliyorum.

Havuçları comes from havuç = carrot.

Here, -lar makes it plural, and the final -ı marks it as a definite direct object.

So:

• havuç = carrot
• havuçlar = carrots
• havuçları = the carrots

Because the speaker is chopping a specific set of carrots, Turkish uses the accusative marker.

This is a very common Turkish pattern. Repeating an adjective or adverb can give the idea of doing something in that manner, often with a sense like into small pieces, little by little, or bit by bit.

So küçük küçük doğramak means:

• to chop into small pieces
• to chop finely
• to cut up small

It sounds natural in Turkish, even though a literal English translation like small small sounds strange.

Doğradıktan sonra means after chopping or more literally after having chopped.

It is built from:

• doğra- = to chop
• -dık = a verbal noun/participle element used in this structure
• -tan = ablative ending, here part of the fixed pattern
• sonra = after

Together, -dıktan sonra is a very common way to say after doing something.

Examples:

• yedikten sonra = after eating
• geldikten sonra = after coming
• doğradıktan sonra = after chopping

Mercimeğin içine means into the lentils or literally into the inside of the lentils.

This is a noun phrase built like this:

• mercimek = lentil
• mercimeğin = of the lentil / of the lentils
• içine = into its inside

So mercimeğin içine is a possessive-type structure:

• X-in içine = into X

Examples:

• çorbanın içine = into the soup
• kutunun içine = into the box
• tencerenin içine = into the pot

You could sometimes say mercimeğe in other contexts, but mercimeğin içine is more explicit: it emphasizes putting something into it.

Two things happen:

1. It takes the genitive ending -in because it is linked to içine.
2. The final k softens to ğ before a vowel.

So:

• mercimek
• mercimeğ-in

This kind of consonant softening is very common in Turkish.

Other examples:

• kitap → kitabın
• çocuk → çocuğun
• renk → rengin

İçine comes from iç = inside/interior.

In this sentence it contains:

• iç = inside
• -i = possessive marker
• -ne / -e = dative, giving the meaning into

So içine means into it / into its inside.

Compare:

• içinde = inside it / in it
• içine = into it
• içinden = out of it / from inside it

Ekliyorum comes from eklemek = to add.

It breaks down as:

• ekle- = add
• -iyor = present continuous
• -um = I

So ekliyorum means:

• I am adding
• or in many contexts simply I add

The subject I does not need to be stated separately, because the verb ending already shows it.

In Turkish, the verb ending usually tells you the subject.

Here:

• ekliyorum = I am adding

Because of -um, the subject is already clear, so ben is usually omitted.

You could say Ben ekliyorum, but that would add emphasis, like:

• I’m the one adding it
• I add it

Turkish normally puts the main verb at the end.

So the sentence structure is very natural for Turkish:

• Havuçları küçük küçük doğradıktan sonra = after chopping the carrots into small pieces
• mercimeğin içine = into the lentils
• ekliyorum = I add

This is one of the biggest word-order differences from English. Turkish often places:

• time expressions first
• objects before the verb
• the main verb last

Yes. This is a very useful pattern.

The structure is:

verb stem + dıktan/diten/duktan/dükten sonra
= after doing ...

Examples:

• kahvaltı yaptıktan sonra = after having breakfast
• eve geldikten sonra = after coming home
• kitabı okuduktan sonra = after reading the book

The vowel changes follow vowel harmony, so the exact form of the suffix changes.

Yes, very much so.

The sequence:

• prepare ingredient
• then add it to something

is exactly the kind of structure used in recipes.

Also, Turkish often uses the present continuous in recipe-style narration:

• doğruyorum = I chop
• ekliyorum = I add
• karıştırıyorum = I stir

Even though it is grammatically I am doing, it can function like instructional or demonstration language.