Start by seasoning the chicken breasts with salt and black pepper on both sides.
In a large skillet, heat the olive oil over medium-high heat. Once hot, add the chicken breasts and cook for about 6-7 minutes on each side, or until they are cooked through and golden brown. Remove the chicken from the skillet and set aside.
In the same skillet, lower the heat to medium and add the minced garlic and red pepper flakes. Sauté for about 1 minute, until fragrant, being careful not to burn the garlic.
Pour in the heavy cream and stir well, scraping up any browned bits from the bottom of the skillet. Bring the mixture to a gentle simmer.
Stir in the grated Parmesan cheese and continue to cook for another 2-3 minutes, until the sauce thickens slightly.
Return the cooked chicken to the skillet, coating it in the creamy sauce. Let it simmer for an additional 2 minutes to heat through.
Serve the chicken hot, garnished with chopped fresh parsley.