In a medium-sized saucepan, bring 3 cups of water to a rolling boil over high heat, with the lid on. Once boiling, remove the lid and gradually whisk in the instant grits, along with 1 teaspoon of salt and 1/2 teaspoon of freshly ground black pepper. Lower the heat to medium-low, stirring occasionally, until the mixture thickens—approximately 5 minutes. Incorporate the Parmesan cheese and 1 tablespoon of butter, stirring until melted. Adjust seasoning with salt and pepper to taste, then cover to keep warm.
While the grits cook, season the shrimp with a pinch of salt and pepper. In a large skillet, melt the remaining 2 tablespoons of butter over medium-high heat. Add the shrimp, minced garlic, and a pinch of cayenne pepper if desired. Cook the shrimp, stirring frequently, until they turn pink and opaque, about 3 to 4 minutes. Remove the skillet from heat, then pour in 2 tablespoons of water, lemon juice, and chopped parsley, stirring until the shrimp are evenly coated with the sauce. Season with additional salt and pepper if needed.
To serve, divide the warm grits into shallow bowls. Place the shrimp and their lemon-garlic sauce over the top of the grits. Accompany each serving with lemon wedges for an extra burst of citrus. Enjoy immediately.