In a mixing bowl, combine halved cherry tomatoes, olive oil, prepared pesto, and balsamic reduction. Sprinkle with kosher salt and black pepper to taste. Stir gently to coat the tomatoes thoroughly, then let the mixture sit for 10 minutes to allow the flavors to meld beautifully.

Season the chicken cutlets liberally with salt and pepper. In an oven-proof skillet, heat a mixture of olive oil and salted butter over medium-high heat until shimmering. Carefully add the chicken cutlets to the skillet and cook for 4-5 minutes on each side, or until they are golden brown and reach an internal temperature of 165°F.

Once the chicken is cooked through, remove the skillet from heat. Spoon the marinated tomato mixture evenly over the chicken cutlets, making sure to scatter the tomatoes generously. Top each cutlet with slices of fresh mozzarella, allowing the creamy cheese to nestle perfectly atop the flavorful tomatoes.

Transfer the skillet to the oven and set it to broil. Broil the casserole for about 3-5 minutes, keeping a close eye on it until the mozzarella is bubbly and beautifully golden on top. If you prefer, you can cover the skillet with a lid and melt the cheese on the stovetop over low heat.

Remove the Caprese Chicken Casserole from the oven and garnish it with large fresh basil leaves for a touch of aromatic flavor. Serve warm alongside toasted ciabatta bread to soak up the delightful juices, creating a comforting and satisfying meal that's sure to impress.