Step 1In a heavy saucepan, bring 4 cups water to a rolling boil with 1 teaspoon salt. Add the grits and stir until smooth. Lower the heat to simmer and cook, stirring often, until the grits are tender and cooked through (1 to 1 1/2 hours for Anson Mills grits). Add more water if the mixture gets too thick and dry.
Step 2While the grits cook, melt 1 tablespoon of the butter in a large skillet over medium heat. Add the garlic and leeks and sprinkle with about one-fourth teaspoon salt. Cook, stirring often, for 5 minutes. Add the remaining butter and the shiitakes and continue cooking and stirring for 10 minutes. Stir in the tamari or soy sauce and the Tabasco.
Step 3When the grits are cooked, add the leek mixture and mix well. Taste and adjust the seasoning. Stir in the Parmigiano-Reggiano and serve.