Preheat the oven to 425°F (220°C) and line the sheet pan with parchment paper for easy cleanup.
In a medium bowl, whisk the eggs until well blended.
In another bowl, mix the grated Parmesan cheese, panko breadcrumbs, garlic powder, onion powder, dried Italian herbs, salt, and pepper.
Place the chicken breasts on the sheet pan. Brush each chicken breast with the beaten egg, then press the mixture of Parmesan and breadcrumbs onto the top of each breast, ensuring they are well-coated.
In a separate bowl, toss the broccoli florets and baby carrots with olive oil, salt, pepper, and paprika (if using) until evenly coated.
Arrange the seasoned vegetables around the coated chicken breasts on the sheet pan.
Bake in the preheated oven for about 25-30 minutes, or until the chicken reaches an internal temperature of 165°F (75°C) and the vegetables are tender.
Once cooked, allow the chicken and vegetables to rest for a few minutes before serving.