Sausage and Cheddar Grits with Fried Eggs

In a medium saucepan over high heat, bring 2 1/2 cups of water to a boil. Add salt, reduce heat to medium and slowly whisk together the grits. Cook uncovered, stirring frequently, until the grits are soft and thickened, about 20 minutes.Using a sharp paring knife, cut off the ends of the sausage casings. Squeeze the sausage pulp and remove the shells. Cook the sausage in a medium-sized skillet over medium-high heat, stirring occasionally with a wooden spoon (to crumble large pieces), until fully cooked, about 5 minutes. Remove the sausages from the pan with a slotted spoon and set aside. Leave the fat that has accumulated in the pan.Remove the grits from the heat and add the cheese and cooked sausage.Return the skillet to medium-high heat. Carefully break the eggs into the pan one at a time. Cook until the whites are set but the yolks are not runny, about 3 minutes. (To make the yolks more firm, turn the eggs over and cook for another 1 minute.) Place the cereal mixture on separate plates and brush each serving with an egg. Serve immediately.