In a food processor or blender purée roasted peppers until smooth. In a large heavy saucepan cook onion in butter over moderately low heat, stirring, until soft, about 5 minutes. Add garlic and cook, stirring, 2 minutes. Stir in grits and add 2 cups milk in a stream, stirring. Simmer mixture, stirring, until milk is absorbed, about 5 minutes. Stir in remaining 2 cups milk and simmer, stirring occasionally, until milk is absorbed, about 5 minutes. Stir in water and gently simmer (do not cover), stirring occasionally, until grits are soft and thickened, about 35 minutes.
Stir in roasted-pepper purée, Tabasco, and salt and pepper to taste. Grits may be made 1 day ahead and chilled, covered, in a buttered 11-inch gratin or other shallow baking dish (about 6-cup). Reheat grits in a 400°F oven until hot, about 15 minutes.