In small bowl combine 2 eggs, milk, salt and pepper and whisk until completely combined.
Heat pan/skillet over medium heat. Melt 1 Tbsp. of butter in pan. Add in beaten eggs occasionally stirring until cooked all the way through then remove and set aside.
Wipe out pan, and place ham slices in. Cook ham for about 3-4 minutes on each side. Again remove and set aside.
Add 1/2 Tbsp of butt in same pan, place one piece of sourdough in pan. Layer American Cheese, eggs, ham, Swiss cheese and top it off the last slice of sourdough.
Cook until golden brown, about 3-4 minutes on each side. I cover mine to help the cheese melt quicker.