ADD rest of butter and tomato paste and vodka if using. Stir. Simmer gently for five minutes.
ADD 1/2 tsp salt and (optional) hot pepper flakes.
ADD half and half, stir.
DRAIN cooked pasta, reserving 1/2 cup cooking water to add to finished dish for more moisture (usually a few TBSP are enough).
ADD pasta to sauce in cooking pan - add reserved pasta water as desired. Mix well.
Sprinkle with cheese and serve. Pass cheese at table.
OPTIONAL - (artichokes/mushrooms) - If using mushrooms and/or artichokes (artichoke hearts best frozen, defrosted and dried off on paper towel): Add remainder of butter and if mushrooms add mushrooms, sautee, stirring frequently for about five minutes. ADD artichokes if using, sauté for a few minutes more.