For the grits: Heat 2 cups water, milk, 1 tablespoon butter, and salt to a gentle boil in a medium saucepan. Sprinkle 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, 15 to 20 minutes.
Meanwhile, prepare tomatoes: Add 1 tablespoon butter to the skillet. Saute onion and garlic until soft and translucent, 2 to 3 minutes. 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 slightly thickened and the tomatoes have broken down, about 10 minutes.
For the shrimp: Heat the remaining tablespoon butter in a large skillet over medium-high heat to sizzling. Add shrimp, season with salt and black pepper, and saute to sear on both sides, about 2 minutes per side.
When grits are thickened, stir in heavy cream and grated Parmigiano-Reggiano cheese. Keep covered with a tight-fitting lid until ready to serve. When tomatoes are ready, remove the skillet from the heat, and stir in the chopped herbs. Cover, and keep warm until shrimp are cooked.
To serve, put a heaping spoonful of grits onto a soup plate. Top with the tomatoes, and arrange the shrimp around the plate. Garnish with freshly shaved Parmigiano-Reggiano cheese.
You can find yellow or white grits in many supermarkets, in textures ranging from coarse to fine. It is best to store your grits in a cool, dry place, preferably a refrigerator or freezer.