Preheat oven to 425°F (220°C). Toss Brussels sprouts with 1 tbsp olive oil, 1/4 tsp salt, and pepper; spread on one side of a rimmed baking sheet.
Whisk remaining olive oil, balsamic, mustard, garlic powder, thyme, and remaining salt. Pat chicken dry and brush or toss with the mixture.
Arrange chicken on the other side of the sheet. Roast 20–25 minutes until chicken reaches 165°F and sprouts are browned, stirring sprouts once halfway.
Optional: transfer chicken to a plate, add broth to the hot pan, scrape browned bits, simmer 1–2 minutes and spoon over chicken.