Die Nudeln bleiben noch kurz im Sieb.

Nudeln is a plural noun here, and the plural definite article in the nominative is die.

• die Nudel = the noodle / one noodle
• die Nudeln = the noodles

Since Die Nudeln is the subject of the sentence, it stays in the nominative plural.

Bleiben means to stay or to remain.

So Die Nudeln bleiben ... im Sieb literally means The noodles stay ... in the colander/sieve.

German often uses bleiben in situations where English might say:

• stay
• remain
• sometimes even sit or be left

Here it suggests that the noodles are left in the sieve/colander for a short time.

Here noch means something like:

• still
• a little longer
• for now
• yet

In this sentence, noch adds the idea that the noodles are staying in the sieve for a bit longer.

So noch kurz together often means:

• for a little while longer
• briefly still

It does not mean another here.

Yes, kurz basically means short, but in this sentence it is used adverbially to talk about time.

So kurz here means:

• briefly
• for a short time
• for a moment

That is very common in German. For example:

• Warte kurz. = Wait a moment.
• Ich komme kurz mit. = I’ll come along briefly.

So in Die Nudeln bleiben noch kurz im Sieb, kurz refers to a short duration.

Im is a contraction of in dem:

• in dem → im

It is used here because the sentence describes a location: the noodles are in the sieve.

With in, German uses:

• dative for location
• accusative for movement toward a place

Here there is no movement being emphasized, just where the noodles remain.

So:

• Die Nudeln bleiben im Sieb. = location → dative
• Ich tue die Nudeln in das Sieb. = movement into it → accusative

It does have one—it’s just hidden inside im.

• im = in dem
• dem is the dative form of das

So:

• das Sieb = the sieve / colander
• in dem Sieb = in the sieve
• im Sieb = same thing, just contracted

German main clauses usually follow the verb-second rule.

The sentence is:

• Die Nudeln | bleiben | noch kurz im Sieb

The finite verb bleiben is in the second position.

This is normal German word order in a statement. Even if you move something else to the front, the verb still stays second:

• Noch kurz bleiben die Nudeln im Sieb.
• Im Sieb bleiben die Nudeln noch kurz.

Those are less neutral than the original, but grammatically they still follow the same rule.

Because kurz is not describing a noun here. It is being used as an adverb.

Compare:

• die kurzen Nudeln = the short noodles
  Here kurzen is an adjective before a noun, so it takes an ending.

• Die Nudeln bleiben kurz im Sieb.
  Here kurz describes the duration of the action, so it is an adverb and has no ending.

That is why it stays simply kurz.

Not always, but very often in everyday cooking contexts, Nudeln is used as a plural mass-like word, similar to how English often says pasta.

You can also have the singular:

• die Nudel = one noodle

But when talking about a serving or a batch, German commonly uses the plural:

• Die Nudeln sind fertig. = The pasta/noodles are ready.
• Ich koche Nudeln. = I’m cooking pasta/noodles.

So this sentence sounds completely natural.

Word-for-word, you might be tempted to do that, but it would sound unnatural in English.

A more natural sense is:

• The noodles stay in the colander a little longer.
• The noodles remain in the sieve briefly.
• The noodles sit in the colander for a moment longer.

The important thing is that noch kurz works together to express a short additional period of time.