Preheat your oven to 400°F (200°C). Line a large sheet pan with parchment paper for easy cleanup.
In a mixing bowl, combine the grated Parmesan cheese, panko breadcrumbs, garlic powder, paprika, salt, and black pepper. Mix well until all ingredients are evenly distributed.
In another bowl, whisk the eggs until fully beaten, then add the olive oil and mix until combined.
Dip each chicken breast into the egg mixture, allowing the excess to drip off. Then, coat it thoroughly with the Parmesan mixture, pressing down gently to help it stick. Place the coated chicken breasts on one side of the prepared sheet pan.
On the other side of the sheet pan, arrange the broccoli florets and baby carrots. Drizzle with a little olive oil and season with salt and pepper to taste; toss lightly to coat.
Bake in the preheated oven for 30 minutes, or until the chicken reaches an internal temperature of 165°F (74°C) and is golden brown. The vegetables should be tender and slightly caramelized.
Remove from the oven and let the chicken rest for a few minutes before slicing. Serve alongside the roasted vegetables.