Press your lips together, add vocal cord vibration, then release.

Americans pronounce brook as BRUUK (/brʊk/). You'll hear it in sentences like "She stood by the brook" or "The bully pushed the bush into the brook" — more examples below.
Record yourself saying "brook" and play it back. The mic stays on your device — nothing's uploaded.
1 syllable, 4 sounds. Explore each sound's mouth shape and how it's made.
Press your lips together, add vocal cord vibration, then release.

Curl or bunch your tongue without letting the tip touch the roof of your mouth. Brace the sides of your tongue against your upper back teeth, and round your lips slightly.
Bring the corners of your lips in slightly so they push forward, but keep them relaxed. Lift the back of your tongue toward the roof of the mouth.

Raise the back of your tongue to touch the soft palate (velum). Stop the air, then release.

The textbook way isn't wrong — it's just not how anyone actually says it.
In "brook", the "k" is not released — the articulators get into position but hold without the burst of air. Air stops but there's no release burst — the articulators hold position.