Layer cheese and ham over 2 slices bread; top with remaining bread.
Beat together milk, egg and nutmeg in a pie plate or shallow dish. Melt butter in a large nonstick skillet over medium heat. Dip each sandwich in milk mixture, turning to coat. Let stand 30 seconds per side to soak up milk mixture.
Melt butter in a large nonstick skillet over medium heat. Add sandwiches; cook 3 minutes per side or until golden brown and cheese is melted. Serve with syrup.