Step 1: Prepare the chicken. Place chicken cutlets between two pieces of plastic wrap and pound them to about ¼-inch thickness. Season both sides lightly with salt and pepper.
Step 2: Set up your breading station. In a shallow dish, place the flour. In another shallow dish, whisk the egg. In a third dish, combine the breadcrumbs and Parmesan cheese.
Step 3: Bread the chicken. Dredge each chicken cutlet in flour, shaking off excess. Dip into the beaten egg, allowing any extra to drip off. Finally, coat thoroughly in the breadcrumb-Parmesan mixture, pressing gently to adhere.
Step 4: Cook the cutlets. Heat ¼ cup olive oil in a large skillet over medium-high heat. Add chicken cutlets in a single layer, being careful not to overcrowd the pan. Cook for 3-4 minutes per side, or until golden brown and cooked through (internal temperature reaches 165°F/74°C). Remove to a plate.
Step 5: Assemble the topping. In a small bowl, combine the halved cherry tomatoes, chopped fresh basil, and minced garlic (if using). Drizzle with a little olive oil, salt, and pepper. Gently toss.
Step 6: Top and serve. Place the warm chicken cutlets on serving plates. Arrange pieces of torn burrata cheese over each cutlet, then spoon the tomato and basil mixture on top. Drizzle with balsamic glaze if desired, and serve immediately.