Brown Sausage:
In a spacious non-stick pan over moderate heat, brown and break up the sausage until fully cooked. Move to a bowl lined with paper towels. Clean the pan.Scramble Eggs:
Return the pan to medium-high heat and melt 2 tablespoons of butter. Pour in the beaten eggs and stir gently until they are softly set and nearly cooked through. Take off the heat.Mix Sausage and Eggs:
Discard the paper towel from the sausage bowl. Fold the scrambled eggs into the sausage until evenly mixed.Butter Bread:
Warm the pan over medium heat. Spread butter on one side of every bread slice.Assemble Sandwich:
Lay one bread slice in the pan, buttered side down. Add a slice of cheese on top. Spoon about ½ cup of the sausage-egg mixture onto the cheese. Place another cheese slice over the filling, then top with a second bread slice, buttered side up.Cook Sandwich:
Cook for 3-4 minutes until the bottom is golden. Carefully turn the sandwich over and cook the other side until golden and the cheese has melted.Serve Sandwich:
Take the sandwich out of the pan and halve it if you like. Repeat with the remaining components. Serve right away.