To make the sandwich, first, scamble the eggs. In a small bowl combine the two eggs, and the milk. Whisk them together until they uniform. Heat a small non-stick skillet over low-medium heat. Add 2 teaspoons of butter of the skillet. Once the butter has melted add the eggs. Season eggs with salt and pepper. Stir the eggs continually until they have set firm. Set aside.
Wipe out the pan, and place the ham slices in the pan. Cook the ham for a couple of minutes, flip the ham, and cook on the other side for an additional 2 minutes. When the ham has heated through set aside.
Build sandwich by buttering one slide of bread, and putting buttered side down into the skillet, then add two slices of American processed cheese, then the eggs, then ham, the Swiss cheese, top with the remaining slice of sourdough bread, and butter the top piece of bread. Cook on low to low-medium heat for 1 to 2 minutes on each side or until the bread is toasted brown. Cut sandwich in half when serving.