In a large non-stick skillet over medium heat, cook and crumble the breakfast sausage until browned and fully cooked. Transfer it to a paper towel-lined bowl to drain excess grease and set aside. Wipe out the skillet.

In the same skillet, melt 2 tablespoons of butter over medium heat. Pour in the beaten eggs. Let them sit for a few seconds, then gently stir to scramble until they’re just set but still soft. Remove from heat.

Discard the paper towel from under the sausage and return it to the bowl. Add the scrambled eggs and gently mix everything together until well combined.

Butter one side of each bread slice. Place one slice, buttered side down, into the skillet. Add one slice of cheese, then about ½ cup of the sausage-egg mixture, another slice of cheese, and top with another slice of bread, buttered side up.

Cook over medium heat for about 3–4 minutes per side, or until the bread is golden brown and the cheese is melted. Press gently with a spatula to help everything meld together.

Transfer to a cutting board, slice in half if desired, and serve immediately. Repeat with remaining ingredients to make 4 sandwiches.