Put two medium-size skillets over medium heat. In one skillet, add a little butter and scramble the two eggs. Salt the eggs to taste. In the other skillet, brown the stack of sliced ham without seperating the slices.
When the stack of ham slices has browned a bit on both sides, remove it from the pan. Butter one side of each sliceof sourdough bread and put one slice into the pan, buttered side down, to grill.
Immediately put the slice(s) of Swiss cheese onto the face-up unbuttered side of the bread that is grilling.
Stack the heated ham slices on the Swiss cheese.
Scoop the scrambled eggs out of the other pan with a large spatuala and place them on the ham.
Place the slice(s) of American cheese on the eggs.
Top off the sandwich with the remaining slice of sourdough bread. Make sure the unbuttered side faces the cheese.
By this time the bread touching the pan should be grilled to a golden brown. Carefully flip the sandwich over and grill the other side for about 2 minutes or until brown.
Slice the sandwich diagonally through the middle and serve with hash browns or French fries on the side.