COOK EGGS: Melt 1 tablespoon salted butter in a medium nonstick skillet over medium-low heat. In a bowl, whisk 8 large eggs until well combined. Pour eggs into the skillet and cook over medium-low heat, gently stirring with a silicone spatula to bring cooked eggs from the edges toward the center. Cook until the eggs are softly scrambled and no liquid egg remains, about 3 to 4 minutes. Remove from heat and set aside.
BUTTER BREAD: Spread the remaining 4 tablespoons salted butter evenly over one side of each of the 8 slices sourdough bread.
TOAST BREAD: Heat a large nonstick skillet or griddle over medium heat. Place the bread slices buttered side down in the skillet.
ADD CHEESE AND HAM: On 4 slices of bread, place 1 slice Swiss cheese and top each with 4 slices thin deli ham. On the remaining 4 slices of bread, place 1 slice American cheese.
MELT AND TOAST: Cook the bread until golden brown and toasted, about 2 to 3 minutes. The cheese should be melted and the ham warmed through.
ADD EGGS: Divide the scrambled eggs evenly among the slices topped with American cheese.
ASSEMBLE SANDWICHES: Place the ham and Swiss halves on top of the egg halves to form 4 sandwiches. Serve with the eggs on top and the ham on the bottom, just like the diner classic.
Notes
Make-Ahead: You can cook the scrambled eggs up to 1 day ahead. Store in the refrigerator and reheat gently before assembling the sandwiches.Storage: Store leftover sandwiches wrapped tightly in the refrigerator for up to 2 days.Reheating: Reheat sandwiches in a skillet over medium-low heat or warm in a 325°F oven for about 10 minutes until heated through.Freezing: Wrap assembled sandwiches tightly in foil and freeze for up to 1 month. Thaw overnight in the refrigerator before reheating.Ingredient Tip: Deli-style thin sliced ham works best because it heats quickly and layers easily on the sandwich.