Cook the Sausage: Heat a large non-stick skillet over medium heat and add the breakfast sausage. Cook, breaking it up with a spoon, until completely browned and no pink remains. Transfer to a paper towel-lined bowl and wipe the skillet clean.
Scramble the Eggs: In the same clean skillet, melt 2 tablespoons of butter over medium-high heat. Pour in the beaten eggs and let them start to set, then gently stir to create fluffy scrambled eggs. Cook until almost no liquid remains, then remove from heat.
Combine Filling: Remove the paper towel from under the sausage and add the scrambled eggs to the bowl with the sausage. Gently mix together to combine the filling. Clean the skillet again and heat over medium heat.
Butter the Bread: Spread butter on one side of each bread slice. This will be the outside of your sandwiches that gets golden and crispy.
Assemble First Sandwich: Place one slice of bread butter-side down in the skillet. Layer with one slice of cheese, about ½ cup of the sausage-egg mixture, another slice of cheese, and top with the second bread slice butter-side up.
Cook the Sandwich: Cook for 3-4 minutes until the bottom is golden brown and crispy. Carefully flip the sandwich and cook the other side for 3-4 minutes until golden brown and the cheese is melted.
Finish and Repeat: Remove to a cutting board and cut in half if desired. Repeat the process with the remaining ingredients to make 3 more sandwiches. Serve immediately while hot and crispy.
