Position a rack in the center of the oven and heat to 425°F. Line a large rimmed sheet pan with parchment. Trim and halve the Brussels sprouts; peel the sweet potato and cut it into 1/2-inch cubes — the small dice is the 30-minute enabler, since larger chunks won't cook through in time.

Toss the Brussels sprouts and sweet potato with 2 tablespoons of the olive oil, 1/2 teaspoon of the salt, and 1/4 teaspoon of the pepper; spread in a single layer. Roast 10 minutes — they get a head start so everything finishes together.

Pat the chicken pieces dry with paper towels. Toss with the remaining 1 tablespoon olive oil, remaining 1/2 teaspoon salt, and remaining 1/4 teaspoon pepper. In a small bowl, whisk the balsamic vinegar, honey, Dijon, and garlic until smooth.

Push the vegetables to one side of the pan — or use a second lined pan — and add the chicken in a single layer. Roast 10 minutes more, until the vegetables are nearly tender and caramelized at the edges.

Brush half the balsamic glaze generously over the chicken pieces. Switch the oven to broil (high); broil 2 minutes, watching closely, until the glaze caramelizes and the largest chicken pieces register 165°F on an instant-read thermometer.

Brush with the remaining glaze, scatter the chopped rosemary or thyme over everything, and serve straight from the pan with any extra glaze drizzled on top.