Put walnuts in a large skillet over medium/high heat. Cook, shaking the pan occasionally, until the nuts are lightly browned and fragrant, 5-8 mins.

Roast brussels with oil and salt and pepper at 400 deg F for 15 mins.
Roughly chop.
In skillet lightly cook garlic - add sprouts
Toss with nuts and cheese and season. Drizzle over with vinegar.