In a nonstick skillet scramble 2 eggs in 1 tsp butter till done to your liking.
Remove eggs and set aside and wipe out skillet.
Assemble the sandwiches with one slice of swiss cheese, 2 slices of ham, 1 scrambled egg, top with another slice of cheese.
Break remaining egg into a bowl with 1 tsp milk and mix well.
Brush the sandwiches liberally with the egg wash with a pastry brush (but don't saturate the bread) and grill over medium/medium high heat in a nonstick skillet in 1 tsp of butter till golden brown. (grill the egg side down first and the melted cheese will help hold the sandwich together when it is time to flip it)Add another tsp butter and flip carefully to grill other side until golden.
Serve with grape jelly or maple syrup on the side.