Create six sandwiches by piling cheese, ham, and more cheese between two slices of bread.
Whisk together eggs, milk, and cinnamon.
Melt 1 Tbsp butter in a large sauté pan over medium heat.
Dip each side of one sandwich in the egg mixture, then place in pan. Grill until bread is golden brown and cheese begins to melt, about 4 minuteseach side.
Repeat with the other 5 sandwiches.
Dust with powdered sugar and serve with maple syrup.