Boil a large pot of water, add a generous pinch of salt, and cook pasta to al dente, according to package directions. Drain and set aside.
While pasta cooks, melt butter in a large skillet over medium-low heat. Add shallots and cook for about 5 minutes, then add garlic and cook 1 minute more. Scrape shallots and garlic out into a blender or food processor, add the drained peppers, and blend until very smooth.
Return the empty skillet to medium-low heat, then add to it the tomato paste, red pepper flakes, and oregano. Cook for 1-2 minutes, stirring frequently. Add broth and cook 1 minute more, scraping the bottom of skillet to release any browned bits.
Stir the blended red pepper sauce into the skillet, bring to a low simmer, then add the cream. Sample a spoonful and add salt and pepper to taste. (I usually add 8-10 cranks of fresh-ground black pepper and about 1/4 teaspoon of kosher salt; my salt-loving husband will add more to his plate.) If you’d like more heat, add an extra sprinkle of red pepper flakes.
Add pasta to the sauce, stir well, and let it rest on the heat for 1-2 minutes. Sprinkle with fresh basil and Parmesan, serve, and enjoy.