Für das Mittagessen brauchst du nur die Süßkartoffel zu schälen und die Aubergine in Scheiben zu schneiden.

Because German main clauses follow the verb-second rule.

Here, Für das Mittagessen comes first, so it takes the first position in the sentence. The conjugated verb brauchst must then come second, and the subject du comes after it.

• Du brauchst nur ...
• Für das Mittagessen brauchst du nur ...

Both are correct; the second one just starts with a different element.

Because für always takes the accusative case.

So:

• für das Mittagessen
• not für dem Mittagessen

Also, Mittagessen is a neuter noun, so its accusative singular article is das.

This is the pattern brauchen + zu + infinitive, which means to need to do something.

So:

• du brauchst ... zu schälen = you need to peel ...
• du brauchst ... zu schneiden = you need to cut ...

In this sentence, both infinitives belong to brauchst:

• die Süßkartoffel zu schälen
• die Aubergine in Scheiben zu schneiden

Together, they mean the things you need to do.

Because after brauchen, German normally uses a zu-infinitive.

Compare:

• Ich brauche die Kartoffel zu schälen.
• Du brauchst die Aubergine zu schneiden.

This is similar to English need to peel / need to cut.

Because they are part of infinitive phrases with zu.

In German, infinitives often go to the end of the clause or phrase, especially after verbs like brauchen, versuchen, beginnen, and so on.

So the structure is:

• brauchst du nur
  • [infinitive phrase at the end]

That is why you get:

• die Süßkartoffel zu schälen
• die Aubergine in Scheiben zu schneiden

Nur means only or just.

Here it limits the whole action that follows:

• brauchst du nur ... = you only need to ...

So the idea is that the task is simple: the only things needed are peeling the sweet potato and slicing the aubergine.

In recipe or instruction language, German often uses the definite article with ingredients, especially when talking about a specific item or a whole ingredient as a unit.

So:

• die Süßkartoffel
• die Aubergine

can mean something like:

• the sweet potato
• the aubergine/eggplant

If the recipe called for more than one, you would probably see the plural:

• die Süßkartoffeln
• die Auberginen

Because German very often forms compound nouns.

Süßkartoffel is one noun made from:

• süß = sweet
• Kartoffel = potato

German writes this as a single word: Süßkartoffel.

The gender comes from the final part, Kartoffel, which is feminine, so:

• die Süßkartoffel

It is a very common German expression meaning to cut into slices.

• in = into
• Scheiben = slices

So:

• die Aubergine in Scheiben schneiden = to cut the aubergine into slices

This is an idiomatic pattern. German often uses:

• in Würfel schneiden = cut into cubes
• in Stücke schneiden = cut into pieces
• in Streifen schneiden = cut into strips

Because this expression is used in a fairly fixed, idiomatic way.

German often omits the article in these result expressions:

• in Scheiben
• in Würfel
• in Stücke
• in Streifen

It is similar to English saying cut into slices, not necessarily cut into the slices.

Because there are two coordinated infinitive phrases:

• die Süßkartoffel zu schälen
• die Aubergine in Scheiben zu schneiden

Repeating zu is very normal and clear. In some coordinated structures, German can omit the second zu, but repeating it is often the safest and most natural choice, especially when the two infinitives each have their own object.

Because und is simply connecting two parallel infinitive phrases.

German usually does not put a comma before und in a straightforward coordination like this:

• ... zu schälen und ... zu schneiden

So the sentence flows as one combined instruction.

Yes, often you could, but the nuance is slightly different.

• Für das Mittagessen = for lunch, in the sense of for the lunch meal / for preparing lunch
• Zum Mittagessen = for lunch / at lunch, often sounding a bit more like as the lunch meal

In many everyday contexts, both would be understandable, but für das Mittagessen emphasizes preparation for that meal.

Because um ... zu means in order to, so it expresses purpose.

But here the sentence is using brauchen + zu-infinitive, which means need to.

So:

• Du brauchst die Süßkartoffel zu schälen. = You need to peel the sweet potato.
• Um das Mittagessen vorzubereiten, schälst du die Süßkartoffel. = In order to prepare lunch, you peel the sweet potato.

So both structures are possible in German, but they do different jobs.