Cook pasta in well-salted water to al dente, about 1 minute shy of doneness. Scoop out 1 ½ cups of pasta water and set aside. Drain pasta.
In your empty pasta pot, heat olive oil and butter over medium heat. Add shallots, garlic, and pepper flakes (½ teaspoon for a moderate kick), and cook until shallots are softened but not brown, about 3 to 4 minutes. Add vodka and cook, stirring up anything stuck, until vodka disappears. Add tomato paste and cook, stirring, for 3 to 4 minutes, until the tomato paste is one shade darker. Add 1 cup of the reserved pasta water, scraping up any stuck tomato paste, stirring until the mixture becomes a sauce. Season it now — I add just about 2 teaspoons kosher salt and many grinds of black pepper — simmer for 2 minutes. Add cream; I begin with ½ cup and then add more, a splash at a time, until I get the shade of orange/pink that I am craving.
Add drained pasta to sauce and toss to coat and adding last ½ cup of reserved pasta water, a splash at a time, as needed to loosen the sauce. Cook pasta and sauce together for 1 minute.
Sprinkle with basil and scoop into bowls, garnishing each with parmesan or pecorino and extra red pepper flakes, to taste. Eat immediately.
