Roast the Peppers: Preheat your oven to 450°F (230°C). Cut the red bell peppers in half, remove seeds and stems, and place them cut side down on a baking sheet. Roast in the oven for about 20-25 minutes until the skin is charred and blistered. Remove from the oven and let cool. Once cooled, peel off the skins and set the roasted peppers aside.
Cook the Pasta: While the peppers are roasting, bring a large pot of salted water to a boil. Add the pasta and cook according to package instructions until al dente. Drain and set aside, reserving about 1 cup of the pasta cooking water.
Make the Sauce: In a blender or food processor, combine the roasted red peppers, heavy cream, minced garlic, olive oil, red pepper flakes, salt, and pepper. Blend until smooth and creamy.
Combine Pasta and Sauce: In a large skillet over medium heat, pour the roasted red pepper sauce and heat it gently. If the sauce is too thick, add a little reserved pasta water until you reach your desired consistency. Add the cooked pasta to the skillet and toss well to coat the pasta evenly with the sauce.
Add Cheese: Remove the skillet from the heat and stir in the grated Parmesan cheese until melted and combined. Adjust seasoning with salt, pepper, and more red pepper flakes if desired.
Serve: Divide the pasta amongst plates and garnish with fresh basil leaves and additional Parmesan, if desired.
Notes
Adjust red pepper flakes to taste for spice level.