Preheat oven to 400°F (200°C). Line a large sheet pan with parchment paper or lightly grease it.
Pat chicken breasts dry. Brush with 1 tablespoon olive oil, then season with garlic powder, smoked paprika, oregano, salt, and pepper. Place in the center of the sheet pan.
In a large bowl, toss broccoli, bell peppers, carrots, and red onion with remaining olive oil, plus a pinch of salt and pepper. Arrange around the chicken.
Roast for 22–25 minutes, or until chicken reaches an internal temperature of 165°F (74°C) and vegetables are tender.
Let the chicken rest for 5 minutes before slicing. Serve with roasted vegetables.