Preheat oven to 400 degrees F.

In a small bowl, add the mozzarella, sliced basil, halved tomatoes, vinegar, 1/4 teaspoon salt, and 1/4 teaspoon pepper. Gently mix to combine. Set aside.

Cut the ends off the zucchini. Cut it in half, lengthwise. Then, cut it into 1/2 inch slices (making a half moon shape). Repeat with the yellow squash.

Tear off two long pieces of aluminum foil (about 1 1/2 feet each). Divide the zucchini and yellow squash between the two pieces of foil, gathering the squash in the middle of each sheet.

Drizzle the squash with the olive oil. Sprinkle the squash with the Italian seasoning. Then, sprinkle with a pinch of salt and pepper. Set aside.

Place one of the chicken breasts on a cutting board and cover it with a piece of plastic wrap. Use a mallet to pound the chicken thin and flat (about 1/2 inch thickness throughout). Repeat with the other chicken breast.

Divide the tomato mixture between the two chicken breasts. Arrange the tomato mixture in a strip 1 inch away from one of the edges of the chicken. Starting with the edge closest to the filling, roll the chicken around the filling. Use 2-3 toothpicks to secure the seam. Try to keep the toothpicks from sticking too far out of the chicken or else they could puncture the foil.

Place the stuffed chicken breasts on top of the squash piles. Sprinkle each chicken breast with a pinch of salt and pepper.

Bring the longest ends of the foil up over the chicken and roll them together. Then roll the short ends in, making sealed packets. Place the packets on a large baking sheet.

Bake for 25 minutes, until the center of the chicken is 165 degrees F. Let them cool for 5 minutes.

Drizzle the chicken with extra balsamic vinegar before serving.