Preheat oven to 425°F (220°C). Line a large sheet pan with parchment paper. Mix all garlic herb butter ingredients in a small bowl and set aside.
Toss the potatoes with 2 tablespoons olive oil, salt, and pepper. Spread on the sheet pan and roast for 15 minutes.
In the same bowl, combine the broccoli, bell peppers, onion, remaining 1 tablespoon olive oil, salt, and pepper. Shake to coat. Keep aside.
Pat the chicken dry. Place it in a zip-top bag with salt, pepper, and half of the garlic herb butter. Seal the bag and toss until the chicken is evenly coated. Remove the pan from the oven, push the potatoes to the sides, and place the chicken in the center. Return to the oven and bake for 10 minutes.
Remove pan from oven and arrange the vegetables around chicken and potatoes. Drizzle everything with the remaining garlic herb butter.
Roast for 15-20 minutes until chicken reaches 165°F (breasts) or 175°F (thighs) and vegetables are tender. Optional: broil for 2-3 minutes for extra crispiness.
Let rest 5 minutes. Garnish with fresh parsley, lemon wedges, and Parmesan if desired.