Season the chicken breasts with salt and black pepper on both sides.
In a large skillet, heat the olive oil over medium heat. Add the chicken breasts and cook for about 6-7 minutes on each side, or until cooked through and golden brown. Remove the chicken from the skillet and set aside.
In the same skillet, add the minced garlic and sauté for about 30 seconds until fragrant.
Pour in the heavy cream and chicken broth, stirring to combine. Bring the mixture to a simmer.
Add the chopped basil and mozzarella cheese to the skillet, stirring until the cheese is melted and the sauce is creamy. If desired, add red pepper flakes for a bit of heat.
Return the cooked chicken to the skillet, spooning the sauce over the top. Let it simmer for an additional 2-3 minutes to heat through.
Serve the creamy mozzarella basil chicken over cooked pasta or rice, garnished with extra basil if desired.