Using a sharp knife, butterfly the chicken breasts by cutting horizontally almost all the way through (you want it to open up like a book with a spine down the center.) Place the chicken between sheets of plastic wrap and pound until about 1/8 inch thick. Season the chicken with salt and pepper.

Heat half of the oil in a large skillet with a lid over medium-high heat. Cook one chicken breast for 3-5 minutes per side or until browned and juices run clear. Top with half of the pesto, spreading it all over the chicken. Top with half of the mozzarella. Cover the pan and cook until the cheese melts, 3-5 minutes. Using a spatula, carefully transfer the chicken to a plate and immediately garnish with half of the tomatoes and red pepper flakes, if using. Repeat with remaining oil, chicken, pesto, mozzarella, and tomatoes and again, transfer to a plate. When done, slice the chicken breasts in half to yield 4 pieces.

Once the chicken is done, immediately add the zucchini noodles to the skillet and toss often until al dente, 3-5 minutes. Drain the noodles into a colander and serve alongside the chicken breasts. Serve.