Start by preheating your oven to 450°F (232°C). Place the whole red bell peppers on a baking sheet and roast for about 20-25 minutes, turning occasionally, until the skins are charred and blistered all over. Alternatively, you can roast them over an open flame on a gas stove or grill if you prefer. Once roasted, transfer the peppers to a bowl and cover tightly with plastic wrap or a lid to steam for 10 minutes — this makes peeling easier.
After steaming, use your hands or a paper towel to gently rub off the charred skins. Remove the stems and seeds, then roughly chop the peppers. Set aside.
While the peppers roast, bring a large pot of salted water to a boil. Add your pasta of choice and cook according to package instructions until al dente. Reserve about 1/2 cup of pasta water before draining.
Heat the olive oil in a skillet over medium heat. Add the minced garlic and sauté for about 1-2 minutes until fragrant but not browned. Stir in the red pepper flakes, salt, and black pepper.
In a blender or food processor, combine the fire-roasted peppers with the sautéed garlic and spices. Blend until smooth and creamy. If necessary, add a splash of the reserved pasta water to thin the sauce to your desired consistency.
Pour the pepper puree back into the skillet and stir in the heavy cream. Simmer gently for 3-5 minutes until the sauce is heated through and slightly thickened. Stir in the grated Parmesan cheese until melted and smooth.
Add the cooked pasta to the sauce, tossing to coat evenly. If the sauce feels too thick, add a little more reserved pasta water to loosen it up.
Divide the pasta among plates and garnish with fresh basil leaves. For an extra touch of indulgence, sprinkle a little more Parmesan on top.