Turn the broiler to high; put the rack 6 inches from the heat. Put 2 TBSP olive oil on a rimmed baking sheet and spread it around; put the baking sheet in the broiler. Meanwhile, core and slice tomatoes. Cut the chicken breasts in half horizontally to make 2 thin cutlets out of each breast. Press down on each with the heel of your hand to flatten.

Carefully remove the baking sheet from the broiler. Put the chicken cutlets on the sheet and sprinkle with salt and pepper. Top with the tomatoes, and broil one side only until the chicken is no longer pink in the center, rotating the pan if necessary for even cooking, 5-10 minutes. Meanwhile grate the mozzarella and Parmesan. Strip 16-20 basil leaves from the stems. Combine the bread crumbs, mozzarella, and Parmesan in a small bowl.

When the chicken is cooked through, remove the baking sheet from the broiler. Lay the basil leaves on top of the tomatoes, sprinkle with the bread crumb and cheese mixture, and drizzle with 3 TBSP olive oil.

Return to the broiler, and cook until the bread crumbs and cheese are browned and bubbly, 2-4 minutes. Serve immediately.