Bring a large pot of heavily salted water to a rolling boil. Cook rigatoni until 1 minute shy of al dente (approx. 9 to 10 minutes). Reserve 1/2 cup of starchy pasta water before draining.

While the pasta cooks, add drained roasted red peppers, heavy whipping cream, vegetable broth, sea salt, and black pepper into a high-speed blender. Blend for 60 seconds until completely silky, smooth, and vibrant orange-red.

Heat olive oil in a large skillet over medium heat. Add minced garlic and red pepper flakes, cooking for 60 seconds until fragrant without browning.

Pour the blended roasted pepper puree directly into the skillet. Simmer gently over medium-low heat for 3 to 4 minutes to marry flavors.

Add the hot drained rigatoni and grated Parmigiano-Reggiano directly into the simmering sauce. Toss vigorously for 1 to 2 minutes, adding splashes of reserved pasta water as needed until the sauce clings luxuriously to every ridge.

Divide pasta into warm shallow bowls. Top each serving with torn creamy burrata, fresh basil, cracked black pepper, and a drizzle of extra virgin olive oil. Serve immediately.