Bring 3 cups of water to a boil in a medium saucepan over high heat, covered. Uncover and slowly whisk in the grits, 1 teaspoon salt, and ½ teaspoon pepper. Reduce the heat to medium-low and cook, stirring occasionally, until thickened, about 5 minutes. Stir in the Parmesan and 1 tablespoon of butter. Remove from the heat and season with salt and pepper. Cover to keep warm.

Meanwhile, season the shrimp with salt and pepper. Melt the remaining 2 tablespoons of butter in a large skillet over medium-high heat. Add the shrimp, garlic, and cayenne, if using, and cook, tossing, until the shrimp are pink, 3 to 4 minutes. Remove from the heat and add 2 tablespoons water, lemon juice, and parsley; stir to coat the shrimp with the sauce and season with salt and pepper.

Divide the grits among shallow bowls and top with the shrimp and sauce. Serve with lemon wedges.