Roast the peppers. Heat the oven to 400°F (200°C). Put whole red peppers on a baking sheet and roast until their skins blacken and blister, about 25–30 minutes. Remove from oven and let them rest until cool enough to handle.

Peel and prep. Slip off the charred skins, discard stems and seeds, and roughly chop the flesh. (If you’re short on time, drained jarred roasted peppers work fine.)

Cook the pasta. Bring a large pot of well-salted water to a boil. Add the pasta and cook until al dente according to package directions. Before draining, scoop out and save about 1 cup of the starchy pasta water. Drain the noodles.

Make the sauce. In a blender or food processor, combine the roasted pepper pieces, heavy cream, minced garlic, salt, pepper, and red pepper flakes (if using). Purée until silky smooth.

Warm the sauce. Heat 1 tablespoon olive oil in a large skillet over medium heat. Pour in the pepper-cream purée and simmer gently for 3–5 minutes, stirring occasionally, until the sauce heats through and the flavors meld. Add a splash of reserved pasta water if the sauce seems too thick.

Toss with pasta. Add the drained pasta to the skillet and toss thoroughly so every strand or tube gets coated. Add more reserved pasta water, a little at a time, until the sauce reaches a glossy, clingy consistency.

Plate and finish. Divide the pasta into bowls. Tear pieces of burrata over each portion so the warm pasta melts into the cheese. Sprinkle chopped basil on top and grate Parmesan if you like. Serve right away.