Bring a generous 2 quarts of water and 1 tablespoon of table salt to boil in a large pot. Using back of the box cooking times as a guide, add pasta, stirring several times at the beginning to prevent sticking, and cook until almost al dente, a couple of minutes shy of the package times. Drain pasta and return it to the pot over low heat.

While pasta water is heating, bring tomato sauce and 3/4 cup of the coconut milk to a simmer in a large (12-inch) skillet over medium-high heat. Continue to simmer, stirring frequently, until a wooden spoon dragged across the skillet bottom leaves a wake in which the sauce is quick to return, about 10 minutes. Stir in the vodka and remaining 1/2 cup of coconut milk and simmer to blend flavors, a couple of minutes longer. Turn sauce into the pot of pasta; continue to cook to rethicken sauce and burn off some of the spirits, a couple of minutes longer. Stir in cheese; continue to cook until cheese dissolves and sauce, except tomato bits, is smooth and creamy, another minute or so. Serve immediately with a sprinkling of cheese, if desired.