Preheat your broiler with the oven rack in the middle position.
Set up a dredging station with three shallow dishes: one for flour, one for egg, and one for breadcrumbs.
Season the chicken cutlets with 1/2 teaspoon of salt and all the pepper. Dredge each piece in flour, then egg, and finally coat in breadcrumbs, pressing lightly to adhere.
Heat 1 1/2 teaspoons of olive oil in a large skillet over medium-high heat. Add 2 chicken cutlets and cook for 1 minute on each side.
Transfer the chicken to a baking sheet coated with cooking spray. Repeat with another 1 1/2 teaspoons of oil and remaining cutlets.
Top each cutlet with shredded mozzarella cheese. Broil in the oven for 1 1/2 minutes or until the cheese is melted and bubbly. Check that the internal temperature reaches 165°F to ensure doneness.
In the same skillet, heat the remaining olive oil over medium-high heat. Add the zucchini, sautéing for 1 minute before adding the cherry tomatoes, garlic, and remaining 1/8 teaspoon of salt.
Cook the vegetables for about 4 minutes, just until softened and lightly caramelized.
Serve the chicken cutlets hot, topped with sautéed vegetables and a generous sprinkle of fresh basil. Enjoy immediately!