In a large non-stick skillet, heat over medium heat and add the ground breakfast sausage. Cook for about 5-7 minutes until the sausage is no longer pink and starts to brown, breaking it into crumbles as it cooks. Once done, transfer the sausage to a paper towel-lined bowl to absorb excess fat and set it aside.

In the same skillet, reduce the heat slightly, and add 2 tablespoons of butter until melted and bubbling. Pour the beaten eggs into the skillet, gently stirring the eggs until they just begin to set, about 2-3 minutes. Remove from heat when they are still slightly undercooked, as they will continue to cook from residual heat.

Mix the cooked sausage with the scrambled eggs in the bowl, ensuring the ingredients are well combined for a flavorful filling.

Butter one side of each slice of sourdough bread generously. In the skillet, place one slice butter-side down, and layer on a slice of cheese. Then, add about ½ cup of the egg and sausage mixture, topping it with another slice of cheese, and finish with another slice of bread, butter-side up.

Cook the assembled sandwich on medium heat for about 3-4 minutes or until the bottom slice is golden brown. Gently press down on the sandwich with a spatula to ensure even grilling and buttery crispness.

Carefully flip the sandwich using a wide spatula, being cautious not to spill the contents. Grill the other side for an additional 3-4 minutes until it becomes golden brown and the cheese has melted.

Once perfectly grilled, remove the sandwich from the skillet, and slice it in half for easy handling. Serve immediately while still warm.