Using a sharp knife, cut open the chicken breasts horizontally, making 4 thinner pieces. Place a piece of plastic wrap over the chicken, and use a meat mallet to even out the thickness to about 1/4-inch thick. Season both sides of the chicken with salt and pepper.

Heat the olive oil in a large skillet over medium-high heat. Add the chicken and cook until browned and no longer pink, 5-6 minutes, flipping once. (You may need to cook the chicken in 2 batches, depending on the size of your skillet. You don’t want to crowd the chicken so that it will brown properly.) Remove the chicken to a plate and cover with foil to keep warm.

Add the chicken broth, onion and tomatoes to the skillet. Use a wooden spoon to scrape up the browned bits on the bottom of the skillet. Bring to a boil, then reduce the heat to medium and let it simmer until reduced to about 1/4 cup, about 10 minutes.

Pour the cream into the skillet. Start adding the butter, one piece at a time, stirring until completely melted before adding another piece. Once all of the butter is added, stir in the Parmesan cheese. Season to taste with salt and pepper.

Serve the tomato parmesan sauce over the chicken. Sprinkle the basil over to serve.