Melt 1 tablespoon butter with olive oil & salt in a 10-inch nonstick skillet until sizzling.
Add eggs and sausage crumbles.
Cook over medium heat, gently lifting and stirring slightly with spatula to allow uncooked portion to flow underneath, for 4-5 minutes or until set.
Remove egg mixture from skillet; keep warm.
Carefully wipe out skillet with paper towel and spread about 1 teaspoon of butter with olive oil & salt onto 1 side of each bread slice.
Assemble sandwiches by topping 1 slice bread, buttered-side down with 1 slice American cheese, 1/4 cooked egg mixture, 1 slice American and 1 slice bread, buttered-side up.
Heat skillet over medium heat.
Place 2 sandwiches into skillet; cooking for 4-6 minutes or until golden brown and the cheese is melted (flip only once).
Remove sandwiches from skillet and keep warm while cooking remaining sandwiches.