Prepare the Grits: In a medium saucepan, bring 4 cups of water to a boil. Add 1 teaspoon of kosher salt. Gradually whisk in 1 cup of stone-ground grits to prevent lumps. Reduce the heat to low, cover, and simmer, stirring occasionally, until the grits are thick and creamy, about 20-25 minutes.

Enhance the Grits: Once the grits have reached a creamy consistency, stir in 2 tablespoons of unsalted butter and 1 cup of shredded sharp cheddar cheese until fully melted and incorporated. Taste and adjust seasoning with additional salt and freshly ground black pepper as needed.

Cook the Eggs: In a non-stick skillet over medium heat, melt the remaining 2 tablespoons of butter. Crack the eggs into the skillet, seasoning with salt and pepper. Cook to your preferred doneness: for sunny-side-up, cook without flipping until the whites are set; for over-easy, flip the eggs gently and cook for an additional minute.

Assemble the Dish: Spoon the cheesy grits into serving bowls, creating a slight well in the center. Place a cooked egg on top of each bowl of grits. Garnish with optional toppings such as cooked bacon crumbles, chopped green onions, or a dash of hot sauce for added flavor.