If the chicken breasts are uneven in thickness, pound them down so they're all even. This will allow all the breasts to cook through evenly. Sprinkle the chicken on both sides with half of the salt and pepper.
In a large 12-inch skillet, heat the olive oil over medium-high heat. Add the chicken and cook for 6-7 minutes, turning once. You want the chicken nice and browned on the outside. (It doesn't have to be cooked all the way through yet.) Set the chicken on a plate.
Reduce the heat to medium. To the skillet, add the crushed tomatoes, garlic, basil, oregano, parsley, red pepper flakes1, and remaining salt2 and pepper. Stir a few times and allow to simmer for 2 minutes. Add the chicken to the sauce and cover with a lid for 3-5 minutes until the chicken is almost done — about 150-155°F. Top each piece of chicken with mozzarella cheese, place the lid back on, and cook for an additional 1-2 minutes until the cheese is melted and the internal temperature of the chicken reaches 160-165°F.2
Serve the chicken with sauce over pasta, crusty garlic bread, a big salad, or even by itself. Leftovers keep well in the refrigerator for up to 4 days. Reheat to your liking.
Make ahead tip: The chicken breasts can be pounded and pre-seasoned for up to 2 days before you're ready to cook it.1Adjust the red pepper flakes to your liking or omit all together. Our house looooves a spicier marinara sauce so I tend to add an additional 1/4-1/2 teaspoon.2Depending on the crushed tomatoes used, additional salt may be needed. Add in 1/4 teaspoon increments.3I typically turn off the heat when the internal temperature of the chicken reaches 160°F and allow the chicken to sit in the skillet for a few minutes to allow it to reach 165°F. This ensures that the chicken won't be over done.