In a bowl, toss together tomatoes, 2 tbsp EVOO, basil, garlic, with salt & pepper to taste. Rest 20 minutes.
Brush tops of bread with the 2 tsp EVOO & season w/ pepper. Toast at 400° for 4 min per side on a baking sheet or in a toaster.
If using 2 (12 oz) chicken breasts then butterfly and cut into 2 portions through the thickness, then pound with a meat mallet to even out pieces. If using 4 (6 oz) pieces then pound each to an even ½-inch thickness.
Dry chicken with paper towels then season both sides with salt, pepper, oregano, and thyme.
Heat 1 tbsp EVOO in a skillet over medium-high heat. Add chicken in a single layer.
Cook until golden brown, about 4 - 5 minutes. Turn top chicken evenly with shredded parmesan and sliced mozzarella. Cook about 4 minutes longer (till 165°).
Off heat add tomato mixture and their juices (the juices will help scrape up those browned bits from the bottom of the pan as you plate it, don't forget to stir them in).
Individually plate each chicken breast (and the tomato topping) slightly overlapping a slice of the bread on serving plates. Drizzle with balsamic glaze immediately before serving.