Preheat oven to 350 degrees F.
Season chicken on both sides with 1 Tablespoon oil, basil, oregano, salt and pepper.
Brown chicken: Heat a large oven-proof skillet over medium-high heat. Once hot, add remaining oil, then chicken, and sear chicken quickly, flipping once, just until golden on both sides. Remove to plate.
Glaze: Mix together the diced red onion, garlic, balsamic vinegar and brown sugar. Pour the mixture into the skillet and simmer, stirring, for 3 minutes.
Bake: Return chicken to pan and spoon sauce over it. Place pan in oven and roast until the chicken is cooked through (165 degrees), about 10-20 minutes depending on how thick the breasts are. Remove from oven.
Turn oven to broil.
Top each chicken with a slice of fresh mozzarella cheese. Broil just until the cheese has melted.
Serve immediately, topped with fresh sliced tomatoes and fresh-cut basil and spoon the pan sauce over the top.
Make it a meal and serve chicken caprese with a green salad and fresh artisan bread.
