Preheat your oven to broil.
Using a sharp knife, slice the chicken in half horizontally to create two, thin cutlets.
Lightly sprinkle both sides of the chicken with salt and pepper and then dust with flour, shaking off the excess.
Heat three tablespoons of olive oil in a large skillet over medium-high heat.
When the oil is hot, place the chicken in the pan and don't move it for 2-3 minutes. You should hear it sizzling, and that's good. If it appears to be cooking too hot, you can turn your heat down a bit.
After 2 minutes, flip the chicken over and cook on the remaining side for two more minutes.
Turn the heat down to low and add the garlic to the pan, sprinkling it all around the chicken. After about a minute, add the chicken broth followed by the butter. Use a spatula to scrape the bottom of the pan and incorporate all those drippings into the sauce.
Remove the pan from the heat and top each piece of chicken with 2-3 tomato slices. Sprinkle the tomatoes with a pinch more salt and pepper, if desired.
Add the mozzarella on top of the tomatoes.
Place the pan on the middle rack of the oven. The chicken is nearly cooked at this point, so you're just browning the tomatoes and cheese to your liking, which was about 5 minutes for me. Since you're broiling, you'll need to watch it close so it doesn't burn.
Remove it from the oven and sprinkle with basil and Parmesan right before serving.