In a large sauté pan, sauté the onions and garlic over medium heat as you normally would until translucent, then add the red pepper and stir.
Stir in the crushed tomatoes and vodka and continue cooking that for 5-7 minutes until reduced a bit, while stirring to prevent it from sticking.
Add the paste, balsamic, salt, and pepper to taste. Reduce the heat to a low simmer and partially cover for about 20-25 minutes or until the volume is reduced by half while giving it an occasional stir.
Stir in the heavy cream, half and half, and basil. Cook until it is warmed through, about 2-3 minutes.
Stir in the grated Locatelli Pecorino Romano cheese.
Separately boil the pasta in salted water, al dente according to package instructions. This will be enough sauce for about 2+ pounds of pasta. Add more grated cheese for serving with additional basil, and crushed red pepper, if desired.