Heat the oven to 425°F with a rack in the middle. Line a large rimmed sheet pan with parchment paper for easier cleanup.

If any Brussels sprouts are very large, cut them in half through the stem so the leaves stay attached and they roast evenly.

Peel the carrots and cut them on a diagonal into pieces about 1/2 inch thick so they cook at the same rate as the sprouts.

Cut the red onion into 1-inch wedges and separate the layers slightly with your fingers.

Put the Brussels sprouts, carrots, and red onion on the sheet pan. Drizzle the vegetables with 2 tablespoons of the oil and sprinkle with 1 teaspoon of the salt.

Toss the vegetables right on the sheet pan until coated, then spread them into a single layer. Turn as many Brussels sprouts cut side down as you can so they brown well.

Roast the vegetables for 10 minutes to give them a head start.

While the vegetables roast, put the chicken thighs in a medium bowl. Sprinkle the chicken with the remaining 1/4 teaspoon salt.

In a small bowl, stir together the hoisin sauce, soy sauce, rice vinegar, grated garlic, grated ginger, and the remaining 1 tablespoon oil until smooth.

Spoon about 3 tablespoons of the glaze into a second small bowl and set it aside for later. Pour the rest of the glaze over the chicken in the medium bowl and turn the chicken so all sides are coated.

Take the sheet pan out of the oven. Use a spatula to stir the vegetables and make open spaces for the chicken.

Put the chicken thighs on the sheet pan smooth side up, nestling them among the vegetables. Scrape any glaze left in the chicken bowl over the tops of the chicken.