Bevor ich den Lauch schneide, wasche ich ihn gründlich unter kaltem Wasser.

Because bevor is a subordinating conjunction, meaning before. In a subordinate clause introduced by bevor, the conjugated verb usually goes to the end.

So:

• Bevor ich den Lauch schneide = Before I cut the leek

This is a very common German pattern:

• weil ich müde bin
• wenn er kommt
• bevor wir essen

In all of these, the finite verb goes to the end of the subordinate clause.

Because the sentence starts with the subordinate clause:

• Bevor ich den Lauch schneide, ...

When that whole clause comes first, it takes up the first position in the sentence. In German main clauses, the conjugated verb must then come in the second position, so you get:

• Bevor ich den Lauch schneide, wasche ich ihn ...

This is called verb-second word order in the main clause.

Compare:

• Ich wasche ihn gründlich, bevor ich den Lauch schneide.
• Bevor ich den Lauch schneide, wasche ich ihn gründlich.

Both are correct, but the word order changes in the second version because the subordinate clause comes first.

Because Lauch is the direct object of schneide. In German, a masculine noun used as a direct object takes the accusative form.

• nominative: der Lauch
• accusative: den Lauch

So:

• ich schneide den Lauch = I cut the leek

If it were the subject, you would use der Lauch instead.

Ihn refers back to den Lauch.

Since Lauch is masculine and is the direct object here, the correct accusative pronoun is ihn.

Forms:

• der → ihn in the accusative

So:

• den Lauch → ihn

That is why German says:

• wasche ich ihn

not:

• wasche ich er
• wasche ich ihm

Lauch usually means leek. In cooking contexts, that is the normal meaning.

In some contexts, Lauch can also be used more generally for a type of allium or, in slang, as a joking insult for a weak or awkward person. But in this sentence, because we are washing and cutting it, it clearly means leek.

Gründlich means thoroughly.

It is an adverb describing how the leek is washed:

• wasche ich ihn gründlich

German adverbs are fairly flexible, but some positions sound more natural than others. In this sentence, gründlich fits well after the object pronoun:

• wasche ich ihn gründlich unter kaltem Wasser

That sounds natural and clear.

Unter kaltem Wasser is the natural expression for washing something under cold water, especially under running water from a tap.

• unter kaltem Wasser = under cold water
• mit kaltem Wasser = with cold water

Both can make sense in some contexts, but here unter is more idiomatic because the idea is that you rinse the leek under the stream of water.

Because Wasser is in the dative here.

With unter, German can use either:

• accusative for movement toward/into a position
• dative for location

Here, the leek is being washed under cold water as a location or setting, so German uses the dative:

• unter kaltem Wasser

Also, Wasser is a neuter noun, and there is no article here, so the adjective takes the ending -em in the dative singular:

• nominative: kaltes Wasser
• dative: unter kaltem Wasser

Because in German, a subordinate clause is separated from the main clause by a comma.

So in:

• Bevor ich den Lauch schneide, wasche ich ihn gründlich unter kaltem Wasser.

the comma marks the end of the bevor clause and the start of the main clause.

German uses commas with subordinate clauses much more consistently than English does.

Yes. German often uses the present tense to describe steps in a process, instructions, habits, or a normal sequence of actions.

So this sentence simply states the order of events:

• first: wash it
• later: cut it

Even though English might also use the present here, learners sometimes expect a special future form. German does not need one in this sentence.

Yes. You can also say:

• Ich wasche ihn gründlich unter kaltem Wasser, bevor ich den Lauch schneide.

This means the same thing.

The main difference is emphasis and word order:

• If the bevor clause comes first, the main clause has inversion: wasche ich
• If the main clause comes first, it stays in normal order: ich wasche

Both versions are completely natural.

Not naturally in this sentence. German usually wants the object or a pronoun if it is important and already known.

So:

• Bevor ich den Lauch schneide, wasche ich ihn gründlich ...

sounds complete and natural.

If you removed ihn, the sentence would sound incomplete, because waschen normally needs an object here: you wash something.

Yes. Bevor introduces a subordinate clause, so it is followed by a clause with its own subject and verb, and that verb goes to the end.

Examples:

• Bevor ich esse, wasche ich mir die Hände.
• Bevor er geht, ruft er an.

So in your sentence:

• Bevor ich den Lauch schneide

is exactly the expected structure.