For the grits: Heat water, milk, and salt to a gentle boil in a medium saucepan. Whisk in the grits. Reduce the heat to simmer, and cook, stirring often with a wooden spoon, until the mixture is smooth, thick, and falls easily from a spoon, about 45 minutes.
Meanwhile, prepare tomatoes: Heat the olive oil in a large skillet. Add onion and sauté and garlic until soft and translucent, 2 to 3 minutes. Add the garlic and cook until fragrant. Pour in white wine, and cook until dry, 2 to 3 minutes. Add bay leaves, and stir in tomatoes and reserved juice. Season with cayenne pepper. Reduce the heat, and simmer until the mixture is slightly thickened, about 10 minutes. Add the shrimp and cook until pink and cooked through, 3 to 5 minutes. Remove the skillet from the heat and stir in the chopped herbs.
When grits are thickened, stir in the Parmigiano-Reggiano. To serve, put a heaping spoonful of grits onto a plate. Top with the tomatoes and shrimp. Garnish with freshly shaved Parmigiano-Reggiano.