Brokuł jest już ugotowany, ale kalafior potrzebuje jeszcze kilku minut.

Jest ugotowany means is cooked or has been cooked in the sense of a resulting state.

• ugotowany = cooked / boiled
• jest ugotowany = is cooked

This is a very common Polish pattern:

• ziemniaki są ugotowane = the potatoes are cooked
• obiad jest gotowy = the meal is ready

Compare:

• ugotował = he cooked
  This is a past-tense verb form, so it would need a subject like on ugotował brokuł = he cooked the broccoli.
• gotowy = ready
  Brokuł jest gotowy is possible, but it means more generally the broccoli is ready, while ugotowany specifically says it has been cooked.

So jest ugotowany is the best choice when the point is that the broccoli has reached the cooked state.

Już usually means already.

So:

• Brokuł jest już ugotowany = The broccoli is already cooked

It tells us that this part is finished now, maybe earlier than expected, or at least before the cauliflower is ready.

A very common contrast in Polish is:

• już = already
• jeszcze = still / yet / more

That exact contrast appears in this sentence:

• broccoli: już ugotowany = already cooked
• cauliflower: jeszcze kilku minut = still needs a few more minutes

Because the verb potrzebować normally takes the genitive case.

So after potrzebuje, we say:

• kilku minut = a few minutes
• not kilka minut

This is one of the most important things to remember with potrzebować:

• Potrzebuję czasu = I need time
• Potrzebujesz pomocy = You need help
• Kalafior potrzebuje kilku minut = The cauliflower needs a few minutes

Here:

• kilka is the basic form
• kilku is the genitive form
• minut is also genitive plural

So the phrase changes because of the grammar required by potrzebować.

Kilku minut means a few minutes.

Base form:

• kilka minut = a few minutes

But after potrzebować, it becomes:

• kilku minut

So in this sentence:

• kalafior potrzebuje jeszcze kilku minut = the cauliflower still needs a few more minutes

This is a very natural expression in Polish for talking about cooking time.

Because it agrees with brokuł, which is a masculine singular noun.

In Polish, adjectives and participles must agree with the noun in:

• gender
• number
• case

Here:

• brokuł = masculine singular
• so: ugotowany

Compare:

• brokuł jest ugotowany = masculine singular
• zupa jest ugotowana = feminine singular
• jajko jest ugotowane = neuter singular
• warzywa są ugotowane = plural

So the ending changes depending on the noun it describes.

Because the sentence has two different verb structures:

1. Brokuł jest już ugotowany
   Here the verb is jest and ugotowany is a participle/adjective describing the state.

2. Kalafior potrzebuje jeszcze kilku minut
   Here potrzebuje itself is the main verb: needs

So we do not need another jest in the second clause.

In English, this difference is also natural:

• The broccoli is cooked
• The cauliflower needs a few more minutes

Yes, a could be possible in some contexts, but ale is better here because there is a clearer contrast.

• ale = but
• a = and / while / whereas

This sentence contrasts two situations:

• the broccoli is ready
• the cauliflower is not ready yet

So ale works very naturally:

• Brokuł jest już ugotowany, ale kalafior potrzebuje jeszcze kilku minut.

If you used a, it would sound a bit softer, more like whereas:

• Brokuł jest już ugotowany, a kalafior potrzebuje jeszcze kilku minut.

That is also grammatical, but ale emphasizes the contrast more strongly.

Yes, and that is exactly why it works.

Jeszcze can mean several related things:

• still
• yet
• more / another

In this sentence:

• potrzebuje jeszcze kilku minut

it means something like:

• still needs a few more minutes

So jeszcze adds the idea that the cauliflower is not ready yet and requires more time.

Very common examples:

• Jeszcze pracuję. = I’m still working.
• Jeszcze nie wiem. = I don’t know yet.
• Potrzebuję jeszcze chwili. = I need one more moment / a little more time.

Yes, brokuł is singular.

In Polish:

• brokuł = a broccoli / a head of broccoli / broccoli
• brokuły = broccoli (plural), depending on context

Polish treats it as a normal countable noun more often than English does.

So:

• Brokuł jest już ugotowany = The broccoli is already cooked

In real usage, whether it refers to one head, one portion, or broccoli as the dish is often understood from context.

Yes. Both are grammatical.

• Brokuł jest już ugotowany
• Brokuł już jest ugotowany

The more neutral and common order is:

• jest już ugotowany

Placing już before jest can add a slight emphasis, but in everyday speech both are possible.

Polish word order is more flexible than English, but not completely free. The version in your sentence sounds very natural and standard.

Ugotowany comes from the perfective verb ugotować.

• gotować = to cook, to boil, to be cooking
• ugotować = to cook completely, to finish cooking

Because ugotowany comes from the perfective verb, it implies a completed result:

• ugotowany = cooked, finished cooking

That matches the meaning of the sentence perfectly: the broccoli has reached the finished state.

If you are learning aspect, this is a good pair to remember:

• gotować → imperfective
• ugotować → perfective

Yes, absolutely.

In Polish, potrzebować can be used with people, animals, objects, food, machines, situations, and so on.

Examples:

• Potrzebuję pomocy. = I need help.
• Samochód potrzebuje naprawy. = The car needs repair.
• Zupa potrzebuje soli. = The soup needs salt.
• Kalafior potrzebuje jeszcze kilku minut. = The cauliflower still needs a few more minutes.

So this use is completely natural.

Yes. It is very natural Polish.

It shows two useful patterns:

1. X jest już ugotowany
   = X is already cooked

2. Y potrzebuje jeszcze kilku minut
   = Y still needs a few more minutes

These are extremely useful for everyday kitchen talk. You can swap in other foods:

• Makaron jest już ugotowany, ale sos potrzebuje jeszcze chwili.
• Kurczak jest już gotowy, ale ziemniaki potrzebują jeszcze dziesięciu minut.

So the sentence is not only correct, but also very practical.