Heat a large skillet over medium heat and add the butter until melted.
Season the chicken breasts with salt and pepper, then sear in the skillet 5 minutes per side until golden and cooked through; remove and set aside.
In the same skillet, sauté the diced onion and minced garlic for 2–3 minutes until softened.
Add the diced roasted red peppers and sauté 1–2 minutes to warm through.
Pour in the chicken broth, add the cream cheese and crushed red pepper, then simmer while stirring until the cream cheese melts and the sauce is smooth.
Return the chicken to the skillet and warm in the sauce for about 2 minutes.
Stir in the chopped basil, adjust seasoning with salt and pepper, then slice and serve the chicken topped with the creamy red pepper sauce.