Learn Dutch: Je moet roeren terwijl je de melk toevoegt. - You must stir while you add the milk.

The word terwijl (while) is a subordinating conjunction. This means it introduces a sub-clause and forces the verb to the very end of that clause. Because of terwijl, the verb moves to the end after de melk.

I learned that toevoegen is a separable verb. Why isn't it split into voegt ... toe here?

You are right, toevoegen (to add) is a separable verb! Normally, in a main clause, it splits (for example: je voegt de melk toe). But because terwijl pushes the verb to the end of the clause, the two parts of the separable verb get pushed back together into a single word: toevoegt.

Why is roeren (to stir) placed right before terwijl, instead of next to moet?

The first part of the sentence (je moet roeren) is a main clause with a modal verb. When you use a modal verb like moeten (must), it takes the second position in the sentence, and the main action verb (roeren) is pushed to the end of that specific clause.

Would the sentence structure change if I used totdat (until) instead of terwijl?