- With the rack in the middle position, preheat the oven to 400°F (200°C).
- In a small saucepan over medium-high heat, brown the onion and garlic in the oil. Add the spices and continue cooking for 30 seconds. Off the heat, stir in the remaining ingredients. Set aside.
- In a 13 x 9-inch (33 x 23 cm) baking dish, place the chicken legs. Drizzle with the sauce. In a second baking dish of about the same size, toss the Brussels sprouts, onions and carrots with the oil. Season with salt and pepper.
- Bake both dishes side by side. Cook the chicken for about 1 hour or until the meat pulls easily from the bone, and cook the vegetables for about 45 minutes or until tender and thoroughly roasted, stirring halfway through cooking.
- Serve the chicken with the vegetables and drizzle with the cooking juices.