In a large skillet, heat the olive oil over medium heat. Add the pancetta and cook, stirring, until the fat has rendered and it's starting to crisp; about 5 minutes. With a slotted spoon, remove the pancetta to a bowl and set aside. Add the tomato paste and the chili pepper paste, stir, and cook until it darkens in color and begins to caramelize; 5-10 minutes. Stir in the garlic and cook for 1 more minute. Add the vodka, stir, and cook until alcohol has mostly evaporated; 3 minutes. Add the peppers and cream, stir, and cook until sauce has thickened; 5-10 minutes. Season with salt and pepper to taste.
Meanwhile, bring a large pot of water to a boil. Once boiling, salt the water. Cook the pasta to 2 minutes less than package directions for "al dente."
Reserve 1 cup of pasta water and drain. Add the pasta to the sauce pan along with the cheese and 1/2 cup of the pasta water. Stir continuously until a thick, glossy sauce forms—adding more pasta water as needed; about 3 minutes. Add the pancetta back to the pan and give it one final stir.
Serve with more cheese and fresh basil.