Learn Hardcore Swedish: Hon vill helst koka soppa i kastrullen, medan han steker grönsaker i stekpannan. - She prefers to boil soup in the pot, while he fries vegetables in the frying pan.

Helst means preferably or most of all.
So Hon vill koka soppa = She wants to cook soup, while Hon vill helst koka soppa = She would rather / most prefers to cook soup.

In a normal main clause, sentence adverbs like helst usually come after the first verb:

Hon vill helst koka soppa.

You can move it for emphasis:

Helst vill hon koka soppa. (More focus on preferably.)
Hon kokar helst soppa i kastrullen. (Focus on the way she usually cooks.)

The given version is the most neutral word order.

Why does vill not end in -r, unlike steker?

Most Swedish present-tense verbs end in -r (for example steker, kokar, pratar).
But vill is the present form of the verb vilja (to want), and it is irregular.

Other common modal verbs behave similarly:

kan (from kunna) – can
ska (from skola) – will / shall / going to
får (from få) – may / is allowed to
måste – must (no -r either)

So hon vill is simply the correct present form: she wants.

What exactly does koka mean here? Is it the same as “to cook”?

Literally, koka means to boil. In cooking, it is often used more broadly for making things that are boiled in liquid, like:

koka soppa – make soup (by boiling it)
koka potatis – boil potatoes
koka kaffe – make coffee

You can also say:

laga soppa – make/prepare soup (more general)
göra soppa – make soup (everyday style)

In this sentence, koka soppa is natural Swedish and suggests making soup by cooking it in boiling liquid.

Why is it i kastrullen and i stekpannan, not i en kastrull or i en stekpanna?

Kastrullen and stekpannan are in the definite form (the saucepan, the frying pan).
Swedish uses the definite form when speakers have a specific item in mind, often something obvious from shared context – for example, the saucepan and the frying pan available in their kitchen.

i kastrullen – in the (known/specific) saucepan
i en kastrull – in a (some, not specified) saucepan

If you said i en kastrull, it would sound like introducing just any saucepan, not the usual one they are using. In a concrete, real-world situation like cooking at home, the definite form is more natural.

How does the definite form work in kastrullen and stekpannan?

Swedish usually marks definiteness with an ending instead of a separate word like the.

en kastrull – a saucepan
- kastrullen – the saucepan
en stekpanna – a frying pan
- stekpannan – the frying pan

Both kastrull and stekpanna are en-words (common gender), so the singular definite adds -en (or -n if the word already ends in -a). That is why we get kastrull + en and stekpanna + n → kastrullen, stekpannan.

Why is it i kastrullen and i stekpannan, not på kastrullen or på stekpannan?

Swedish uses i (in) for things that are inside a container or vessel:

i kastrullen – in the saucepan
i stekpannan – in the frying pan
i ugnen – in the oven

På (on) is used for surfaces:

på bordet – on the table
på tallriken – on the plate

Food is inside the pot/pan, so i kastrullen and i stekpannan are correct.

What does medan mean here, and does it always mean “at the same time”?

Medan normally means while, and it introduces a subordinate clause:

Hon vill helst koka soppa i kastrullen, medan han steker grönsaker i stekpannan.
→ She prefers to cook soup … while he is frying vegetables …

It often implies simultaneity, but it can also have a slight contrastive meaning, close to whereas:

Hon älskar att laga mat, medan han hatar att diska.
→ She loves cooking, whereas he hates doing the dishes.

The exact nuance depends on context; here it naturally means that the actions happen at the same time.

Why is the word order medan han steker grönsaker, not medan steker han grönsaker?

Swedish main clauses normally have verb-second word order:

Han steker grönsaker. (subject–verb–object, but if you move something to the front, the verb must still be in second position)

In subordinate clauses (clauses introduced by medan, att, eftersom, etc.), the word order is different: the subject comes before the verb and there is no verb-second rule:

medan han steker grönsaker – while he fries vegetables

So:

Main clause: Han steker grönsaker.
Subordinate clause: medan han steker grönsaker (not medan steker han grönsaker).

What does steker mean exactly, and how is it different from other cooking verbs?

Steker is the present form of steka, which means to fry in a pan with fat (oil, butter, etc.). You typically steker things like:

steka grönsaker – fry vegetables
steka kött – fry meat
steka pannkakor – fry pancakes

Some related verbs:

fritera – deep-fry (in a lot of oil)
grilla – grill or barbecue
woka – stir-fry in a wok
fräsa – quickly fry/sauté on relatively high heat (often used with onions, spices, etc.)

In this sentence, steker grönsaker is standard for frying vegetables in a frying pan.

What does grönsaker mean grammatically? Is it singular or plural, and what is the singular form?

Grönsaker is the indefinite plural form of grönsak (vegetable):

en grönsak – a vegetable
grönsaken – the vegetable
grönsaker – vegetables
grönsakerna – the vegetables

In the sentence, han steker grönsaker means he is frying vegetables (some, not specified which ones). If you wanted to say the vegetables, you would say han steker grönsakerna.