Preheat oven to 425°F and line a large sheet pan with parchment paper.
Add diced russet potatoes to the pan and toss with olive oil, salt, Italian seasoning, and black pepper. Spread evenly and roast for 15 minutes, flipping once halfway through.
Remove the pan and add broccoli, carrots, and red onion. Toss gently and return to the oven for 5 minutes.
While the vegetables roast, whisk the egg in a shallow bowl. In another bowl, mix Parmesan, garlic powder, Italian seasoning, salt, pepper, and paprika.
Dip chicken into the egg, then press firmly into the Parmesan mixture until fully coated.
Remove the pan from the oven and push vegetables to the sides. Place chicken in the center and lightly drizzle or brush with olive oil.
Bake for 20–25 minutes, or until chicken reaches 165°F internally and the coating is golden.*Optional: Broil for 1–2 minutes for extra crispiness. Let rest briefly, then serve warm.