Preheat the oven to 400°F (200°C). Lightly grease a 9x13-inch baking dish.
Pat the chicken breasts dry. If they are very thick, gently pound them to an even thickness.
Season both sides of the chicken with Italian seasoning, garlic powder, paprika, salt, and black pepper.
Spread basil pesto evenly over the top of each chicken breast.
Place the pesto-coated chicken in the prepared baking dish.
Arrange the cherry tomatoes around the chicken and drizzle them lightly with olive oil.
Bake for 20–25 minutes, depending on the thickness of the chicken, until the chicken reaches an internal temperature of 165°F (74°C).
Remove the baking dish from the oven and sprinkle mozzarella and Parmesan over the chicken.
Return to the oven and bake for another 5 minutes, until the cheese is melted and lightly golden.
For extra browning, broil for 1–2 minutes, watching carefully.
Remove from the oven and let the chicken rest for 5 minutes.
Garnish with fresh basil and serve with lemon wedges.