In a gallon-size resealable plastic bag or shallow bowl, combine the chicken and buttermilk. Marinate for 30 minutes to 1 hour.
Preheat the oven to 400 degrees F. Place the bread crumbs in a shallow bowl. Remove the chicken from the buttermilk marinade and dredge them in the bread crumbs, pressing to coat both sides.
In a large nonstick skillet, heat the olive oil over medium-high heat. Add the chicken and cook, just until browned on both sides, 3 to 4 minutes total. Remove the chicken to a baking sheet lined with parchment. Bake for 12 minutes, then take the chicken out of the oven and divide the sauce and mozzarella among them. Return the chicken to the oven and bake until the sauce is warm and the cheese melts, 4 to 6 minutes.
Sprinkle each chicken breast with fresh basil and serve with pasta or, for a really low-cal option, Shirataki noodles!