Mix the egg whites and milk together in a large bowl until well combined.
Spread honey mustard evenly on 4 slices of bread.
Layer Swiss cheese and ham on the mustard-covered bread, then top with remaining bread slices to form 4 sandwiches.
Dip each sandwich in the egg mixture, coating both sides thoroughly.
Spray a large nonstick skillet with cooking spray and heat to medium-high.
Place sandwiches in the skillet and cook until golden brown, approximately 3-4 minutes per side.
Flip sandwiches carefully and cook the other side until golden brown.
Remove from heat, sprinkle with powdered sugar, and serve immediately with raspberry jam on the side.