Preheat your oven to 400°F (200°C).
Make a horizontal slit in each chicken breast to create a pocket. Be careful not to cut all the way through.
Stuff each chicken breast with 2 tablespoons of basil pesto.
In a large bowl, toss the cherry tomatoes, baby carrots, and broccoli florets with olive oil, salt, and pepper.
Place the stuffed chicken breasts and the seasoned vegetables on a baking sheet or in an oven-safe dish.
Roast in the preheated oven for about 20-25 minutes or until the chicken is cooked through (internal temperature of 165°F or 74°C) and the vegetables are tender.
Sprinkle with grated Parmesan cheese before serving.