Hún saxar brokkolíið smátt og setur blómkálið í stóran pott.

Because Icelandic usually puts the definite article onto the end of the noun instead of using a separate word like English the.

• brokkolí = broccoli

• brokkolíið = the broccoli

• blómkál = cauliflower
• blómkálið = the cauliflower

The ending -ið here is the definite article for a neuter singular noun.

Icelandic normally uses a suffixed definite article, not a separate word before the noun.

So instead of:

• the broccoli
• the cauliflower

Icelandic says:

• brokkolíið
• blómkálið

A separate word equivalent to the can exist in some contexts, but the normal everyday pattern is the ending attached to the noun.

Saxar is the present tense of the verb að saxa, which means to chop, to mince, or to cut up finely.

In cooking, að saxa is very common for chopping ingredients into small pieces.

So Hún saxar brokkolíið means she is chopping the broccoli.

Smátt means something like finely or into small pieces here.

Although smár/smátt is originally an adjective meaning small, Icelandic often uses the neuter singular form of an adjective in an adverb-like way. In cooking language, this is very common.

So:

• saxa smátt = chop finely / chop into small pieces

It is not describing the broccoli as grammatically neuter here in the same way an ordinary adjective would. It is more describing how the chopping is done.

Because í can take either the accusative or the dative, depending on meaning.

• accusative = movement into something
• dative = location in something

Here the cauliflower is being put into the pot, so there is movement toward an inside location. That is why Icelandic uses the accusative:

• í stóran pott = into a big pot

If you were talking about something already being inside the pot, you would use the dative:

• í stórum potti = in a big pot

Stóran agrees with pott.

The noun pottur is:

• masculine
• here in the accusative singular
• indefinite

So the adjective stór has to match that, giving:

• stóran pott = a big pot

This is a basic Icelandic rule: adjectives agree with the noun in gender, number, case, and also whether the form is strong or weak.

Pottur is the nominative singular form, the dictionary form.

But after í with movement, the noun goes into the accusative, and the accusative singular of pottur is pott.

So:

• pottur = a pot
• í pott = into a pot

This kind of change is very common with masculine nouns in Icelandic.

Setur is the present tense of að setja = to put, to place.

The verb að setja is irregular enough that its present singular form is:

• ég set
• þú setur
• hann/hún/það setur

So hún setur means she puts.

It is simply the normal 3rd person singular present form.

Because the same subject, hún = she, applies to both verbs:

• Hún saxar ...
• og setur ...

In English we can also do this:

• She chops the broccoli and puts the cauliflower into a big pot.

So Icelandic does not need to repeat hún before setur.

The first clause has normal straightforward word order:

• Hún = subject
• saxar = verb
• brokkolíið = object
• smátt = adverb-like word

Then:

• og = and
• setur = verb
• blómkálið = object
• í stóran pott = prepositional phrase

This is a very natural sentence pattern in Icelandic. Icelandic often follows a verb-second rule in main clauses, and here that rule is satisfied because the verb comes right after the subject.

Yes. In this sentence both are treated as neuter singular nouns:

• brokkolí
• blómkál

That is why the definite form ends in -ið:

• brokkolíið
• blómkálið

Knowing the gender is important because it affects articles, adjectives, and sometimes pronouns.

Because the sentence is talking about:

• the broccoli
• the cauliflower

but only a big pot, not a specific previously identified pot.

So Icelandic marks the first two nouns as definite:

• brokkolíið
• blómkálið

But leaves pott indefinite:

• í stóran pott = into a big pot

That difference works much like English:

• the broccoli
• the cauliflower
• a big pot

Not naturally in this sentence. A literal word-for-word translation might suggest small, but in actual use here it means something more like:

• finely
• into small pieces

So Hún saxar brokkolíið smátt is better understood as:

• she chops the broccoli finely

rather than:

• she chops the broccoli small

English and Icelandic do not always use the same kind of word in these cooking expressions.