Cut the red bell peppers in half, remove the seeds, and place them cut-side down on a baking sheet. Roast in the oven for about 20-25 minutes until their skins are charred and blistered.
Remove the peppers from the oven and place them in a bowl, covering it tightly with plastic wrap. This will steam the peppers and make it easier to peel the skin. Let them sit for about 10 minutes.
While the peppers are steaming, cook the pasta according to package instructions until al dente. Drain and set aside, reserving 1/2 cup of pasta water.
After the peppers have cooled, peel off the skin and chop them into smaller pieces.
In a blender or food processor, combine the roasted red peppers, heavy cream, garlic, oregano, smoked paprika, salt, and pepper. Blend until smooth and creamy.
In a large skillet, heat olive oil over medium heat. Pour the creamy red pepper sauce into the skillet and bring to a simmer. Stir in the reserved pasta water as needed to achieve your desired sauce consistency.
Add the cooked pasta to the skillet, tossing to coat the pasta evenly with the sauce.
Stir in the grated Parmesan cheese, allowing it to melt and incorporate into the sauce. Adjust seasoning with salt and pepper as desired.
Serve immediately, garnished with fresh basil leaves.
Notes
For a spicier kick, add red pepper flakes to the sauce.