Min søster vil hellere have rugbrød med skinke og peberfrugt end varm suppe i dag.

With a possessive like min, Danish normally uses the noun in its basic indefinite form: min søster, min bil, mit hus.

So:

• søster = sister
• søsteren = the sister
• min søster = my sister

You do not combine min with the definite ending -en here.

In Danish, a present preference is very often expressed with vil hellere:

• Jeg vil hellere have te = I’d rather have tea

So even though English uses would, Danish usually uses present-tense vil in this kind of sentence. It is the normal, idiomatic way to express a current preference.

Because each word has a different job:

• vil = the finite/modal verb
• hellere = an adverb meaning rather
• have = the infinitive main verb

In a normal Danish main clause, the finite verb comes early, and adverbs like hellere usually come after it. Then the infinitive follows the modal verb.

So the pattern here is:

subject + finite verb + adverb + infinitive

That gives Min søster vil hellere have ...

Because have is very natural in Danish when talking about food and drink choices.

Compare:

• vil have rugbrød = wants to have some rye bread
• vil spise rugbrød = wants to eat rye bread

Both can work, but have is especially common when someone is choosing what they want. It works much like English have in sentences such as I’ll have soup or She wants to have a sandwich.

Because rugbrød is being used as a general food item, not as one specifically identified object.

Danish often leaves out the article with foods and substances when speaking generally:

• drikke kaffe
• spise brød
• have suppe
• have rugbrød

So rugbrød here means rye bread as food, not the rye bread or a rye bread loaf.

For the same reason: they are ingredients, named in a general way.

med skinke og peberfrugt means with ham and bell pepper as toppings or fillings. Danish commonly uses bare nouns like this for ingredients, especially in food descriptions.

It does not mean something like with a ham and a pepper.

End is the word used after a comparative expression to mean than.

Here the comparative idea comes from hellere:

• hellere X end Y = rather X than Y

So:

• hellere have rugbrød ... end varm suppe

means that one option is preferred over the other.

Because suppe is a common-gender noun: en suppe.

In Danish adjective agreement:

• common gender, singular, indefinite: varm
• neuter, singular, indefinite: varmt
• plural or definite forms: varme

So:

• en varm suppe = correct
• et varmt hus = neuter example
• den varme suppe = definite example

That is why varm suppe is correct here.

Yes. One med can introduce a whole list joined by og.

So med skinke og peberfrugt means:

• with ham
• and bell pepper

You do not need to repeat med before the second noun.

I dag is a time expression, and putting it at the end is very natural and neutral.

Yes, it can also be moved for emphasis:

• I dag vil min søster hellere have rugbrød med skinke og peberfrugt end varm suppe.

That version puts more focus on today.

When something like i dag is moved to the front in Danish, the finite verb still stays in second position. That is why it becomes I dag vil min søster ..., not I dag min søster vil ...

A useful breakdown is:

• Min søster = subject
• vil = finite verb
• hellere = adverb of preference
• have = infinitive main verb
• rugbrød med skinke og peberfrugt = the preferred option
• end varm suppe = the option being compared against
• i dag = time expression

So the sentence follows a very typical Danish main-clause pattern, with the finite verb early in the sentence and the rest built around it.