Preheat oven to 425°F (220°C). Line a half sheet pan with parchment paper or aluminum foil.
Toss halved potatoes with 1.5 tablespoons olive oil, half the ranch seasoning, ½ teaspoon paprika, salt, and pepper. Spread cut-side down on one half of the prepared pan and roast for 10 minutes.
Toss bell peppers and red onion wedges with 1 tablespoon olive oil, salt, and pepper. Set aside until potatoes have had their 10-minute head start.
Pat chicken breasts completely dry. In a small bowl, combine remaining ranch seasoning, remaining paprika, garlic powder, and onion powder. Drizzle chicken with remaining ½ tablespoon olive oil, then coat evenly with the seasoning mixture.
After potatoes have roasted for 10 minutes, remove pan from oven. Push potatoes to one side, add seasoned bell peppers and onions in a single layer, and place seasoned chicken breasts in the center with space around each piece.
Roast at 425°F (220°C) for 22-28 minutes until chicken reaches 165°F (74°C) internal temperature and potatoes are fork-tender. For extra browning, broil for the last 2-3 minutes.
Remove from oven and let chicken rest on the pan for at least 5 minutes. Garnish with fresh parsley and serve directly from the sheet pan.