Set your oven to 425°F (220°C) and get a large baking sheet ready.
Dry the chicken pieces thoroughly with paper towels to help the skin crisp up nicely.
In a bowl, combine the minced garlic, olive oil, paprika, thyme, salt, and black pepper, then evenly coat the chicken with this mixture.
In a separate large bowl, toss the broccoli, carrots, red bell pepper, and onion with olive oil, salt, and pepper until everything is well coated.
Spread the vegetable mix in a single layer on the baking sheet and then arrange the chicken pieces on top, skin side up.
Place the baking sheet in the oven and roast for 35 to 40 minutes, or until the chicken reaches an internal temperature of 165°F (74°C) and the vegetables are tender and slightly caramelized.
If you want extra-crispy chicken skin, switch the oven to broil and cook for an additional 2 to 3 minutes, watching carefully.
Remove the pan from the oven, let the chicken rest for five minutes, then garnish with fresh rosemary or parsley before serving warm.