Season the chicken breasts evenly with salt and black pepper on both sides.
In a large skillet, heat olive oil over medium-high heat.
Add the chicken to the skillet and sear for 5 to 7 minutes per side until the internal temperature reaches 165°F (74°C).
Remove the chicken from the skillet and transfer to a plate; tent with foil to keep warm.
Reduce skillet heat to medium and add minced garlic, sautéing for 60 seconds until fragrant.
Pour in the chicken broth and use a wooden spoon to deglaze the pan by scraping up any browned bits.
Stir in the heavy cream and bring to a light simmer for 3 to 5 minutes until the sauce begins to reduce and thicken.
Whisk in the Parmesan cheese and red pepper flakes until the cheese is melted and the sauce is smooth.
Fold in the julienned basil leaves.
Return the chicken to the skillet and spoon the basil cream sauce over the meat before serving.