Im Spülbecken liegt ein Schneidebrett, das ich nach dem Kochen noch abwaschen muss.

German often puts a place, time, or other detail first for emphasis. The finite verb still has to stay in second position in a main clause.

So:

• Im Spülbecken = first element
• liegt = second element
• ein Schneidebrett = subject, which comes after the verb

This is normal German word order. The basic version would be:

• Ein Schneidebrett liegt im Spülbecken.

But starting with Im Spülbecken highlights the location: In the sink, there is a cutting board.

Im is just the common contraction of in dem.

• in dem → im

So:

• im Spülbecken = in the sink

This contraction is extremely common in everyday German.

German often uses specific position verbs where English would simply use is.

Here, liegen means to lie / to be lying and is used for things that are:

• horizontal
• flat
• not standing upright

A cutting board is thought of as lying flat in the sink, so:

• Im Spülbecken liegt ein Schneidebrett.

Compare:

• Das Buch liegt auf dem Tisch. = The book is lying on the table.
• Die Flasche steht auf dem Tisch. = The bottle is standing on the table.

So liegt sounds more natural than just using ist.

Because ein Schneidebrett is the subject of the sentence, so it must be in the nominative case.

Even though it comes after the verb, it is still the subject.

• ein Schneidebrett = nominative
• Schneidebrett is neuter, so nominative singular is ein

If it were a direct object, then you would look for the accusative form, but here it is the thing that lies in the sink.

Das is a relative pronoun meaning that / which.

It refers back to ein Schneidebrett:

• ein Schneidebrett, das ...
• a cutting board that ...

Since Schneidebrett is neuter, the relative pronoun is das.

Inside the relative clause, das is also the object of abwaschen:

• das ich ... abwaschen muss
• that I still have to wash

So here das connects the noun to more information about it.

Because das and dass do different jobs.

• das = that/which as a relative pronoun, or the/that as an article/demonstrative
• dass = that introducing a content clause

Here it refers back to ein Schneidebrett, so it must be das:

• ein Schneidebrett, das ich ... abwaschen muss

A dass clause would look more like:

• Ich weiß, dass ich das Schneidebrett abwaschen muss.
• I know that I have to wash the cutting board.

Because das ich nach dem Kochen noch abwaschen muss is a relative clause, and German normally sets relative clauses off with commas.

So the comma marks the start of extra information about ein Schneidebrett.

This is required in standard German spelling.

It is at the end of the relative clause, which is a kind of subordinate clause. In German subordinate clauses, the finite verb usually goes to the end.

Relative clause:

• das ich nach dem Kochen noch abwaschen muss

Structure:

• das = relative pronoun
• ich = subject
• nach dem Kochen = time phrase
• noch = still / yet
• abwaschen = infinitive
• muss = finite modal verb, at the end

This is normal German subordinate clause word order.

Because abwaschen is a separable verb.

In a simple main clause, it separates:

• Ich wasche das Schneidebrett ab.

But when you use it with a modal verb like müssen, the full infinitive stays together at the end:

• Ich muss das Schneidebrett abwaschen.

And inside this relative clause:

• ..., das ich ... abwaschen muss.

So the infinitive abwaschen remains one word.

Here noch means something like:

• still
• yet
• remaining to be done

So:

• das ich nach dem Kochen noch abwaschen muss
• that I still have to wash after cooking
• that I have yet to wash after cooking

It suggests the washing has not been done yet.

Nach means after, and it takes the dative case.

So:

• nach dem Kochen = after the cooking / after cooking

Here Kochen is being used like a noun, so it is capitalized.

• das Kochen = the act of cooking

That is why you get:

• nach + dem + Kochen

Because it is a nominalized verb—a verb being used as a noun.

• kochen = to cook
• das Kochen = cooking, the act of cooking

In German, nouns are capitalized, so Kochen gets a capital K here.

Yes, but the meaning changes slightly.

• nach dem Kochen = after cooking
• nach dem Essen = after eating

In your sentence, nach dem Kochen focuses on the time after preparing food. If you say nach dem Essen, it would mean the board still needs washing after the meal itself.

Both are grammatical; they just refer to different moments.

Not exactly.

• Spülbecken usually means a kitchen sink
• Waschbecken usually means a bathroom sink / washbasin

So in this sentence, Spülbecken is the natural choice because a cutting board belongs in the kitchen.

Yes. Das Schneidebrett is neuter.

That is why you see:

• ein Schneidebrett
• das ich ... abwaschen muss

The relative pronoun das agrees with Schneidebrett in gender and number.

Yes. A natural English translation could be:

• There is a cutting board in the sink that I still have to wash after cooking.

German does not need a dummy there the way English often does. It simply says:

• Im Spülbecken liegt ein Schneidebrett ...

So the German structure is different, but the meaning matches very well.