Preheat your oven to 400°F and slice the peppers in half, removing the seeds and stems. Place them cut-side down on a baking sheet and drizzle with a tablespoon of olive oil. Roast for 25 to 30 minutes until the skins are blistered and charred.

Once roasted, let the peppers cool before peeling away the charred skin. Set the peeled pepper flesh aside.

Bring a large pot of salted water to a boil. Add the pasta and cook until al dente, according to package instructions. Reserve 1 cup of pasta water before draining.

In a blender, combine the roasted peppers, minced garlic, heavy cream, and remaining olive oil. Blend until smooth, adjusting with salt and pepper.

Pour the sauce into a skillet over medium heat. Stir in the grated Parmesan cheese and let it melt into the sauce.

Add the drained pasta to the skillet and toss to coat. If too thick, add some reserved pasta water. Stir in fresh basil at the end.