Add the chicken broth, whole milk, butter, salt, black pepper, and garlic powder to a medium saucepan. Bring the mixture to a light boil over medium heat, stirring occasionally to keep the milk from scorching.

Slowly whisk in the grits. Reduce the heat to low and cook, stirring frequently, until very thick and creamy. Quick grits will take approximately 5 to 7 minutes, while stone-ground grits may take 20 to 25 minutes. Remove the saucepan from the heat and stir in the cheddar and smoked gouda until completely melted.

Lightly grease a baking dish or sheet pan. Spread the hot grits into an even layer approximately 1 inch thick. Cover and refrigerate for at least 2 hours, or until completely cold and firm enough to cut. For easier preparation, chill them overnight.

Cut the chilled grits into equal squares, rectangles, or rounds. Place the flour in one shallow bowl. In a second bowl, beat the eggs with the milk or water. In a third bowl, combine the breadcrumbs, Cajun seasoning, garlic powder, and smoked paprika. Coat each grit cake in flour, dip it into the egg mixture, and press it into the seasoned breadcrumbs.

Heat approximately 1/2 inch of frying oil in a heavy skillet over medium-high heat until it reaches about 350°F. Fry the grit cakes in batches for 2 to 3 minutes per side, or until crisp and golden brown. Transfer them to a wire rack or paper towel-lined plate and season lightly with salt while hot.

Pat the shrimp dry and season them with Cajun seasoning, smoked paprika, and garlic powder. Heat the olive oil in a large skillet over medium-high heat. Arrange the shrimp in one layer and cook for 1 to 2 minutes per side, just until pink and beginning to curl. Transfer the shrimp to a plate to prevent overcooking.

Reduce the heat to medium and melt the butter in the same skillet. Add the garlic and cook for about 30 seconds, stirring constantly. Pour in the chicken broth, lemon juice, and hot sauce, if using. Simmer for 2 to 3 minutes, scraping the flavorful browned bits from the bottom of the skillet.

Return the shrimp to the skillet and toss briefly in the garlic butter sauce until fully cooked and coated. Turn off the heat and stir in the parsley and green onions. Place two fried grit cakes on each plate, spoon the shrimp and sauce over them, and serve immediately.