Boil pasta in salted water according to package instructions until al dente. Reserve ½ cup pasta water, then drain.
In a blender or food processor, combine roasted red peppers, sun-dried tomatoes, and a splash of pasta water. Blend until smooth.
In a large skillet, heat olive oil over medium heat. Sauté garlic and shallots until fragrant (1–2 min).
Pour in the red pepper-tomato puree, stir in heavy cream, and simmer 3–5 minutes.
Stir in Parmesan, season with salt and pepper. Adjust consistency with reserved pasta water if needed.
Toss cooked pasta in the sauce until evenly coated.
Transfer pasta to serving plates or a shallow baking dish.
Tear burrata over the top. Optional: place under broiler for 1–2 minutes for a lightly melted effect.
Drizzle with olive oil or balsamic glaze and sprinkle fresh basil on top.
Serve immediately with crusty bread to soak up the creamy sauce.
