Preheat the oven to 400°F (200°C). Line a baking sheet with aluminum foil and lightly coat with nonstick spray.
Trim chicken breasts if needed. Cut 3 to 4 horizontal slits in each breast to form pockets, taking care not to cut all the way through.
Prepare vegetables: slice the yellow squash, zucchini, and roma tomatoes into 1/4-inch rounds.
Stuff each chicken pocket with one slice of yellow squash, one slice of zucchini, and one slice of tomato.
In a small bowl, mix the olive oil and minced garlic. Brush the tops of the stuffed chicken with the garlic oil and season evenly with kosher salt and black pepper.
Bake the chicken on the prepared sheet for about 10 minutes.
Remove the pan from the oven, sprinkle 1/2 cup shredded mozzarella evenly over the chicken, then return to the oven and bake another 10 minutes or until the chicken is cooked through and the cheese is melted.
Let the chicken rest briefly, then serve hot.