Preheat oven to 350 degrees.

Beat egg whites and milk in a shallow dish.

Assemble sandwiches by spreading honey mustard on bread slices. Place 3 slices of Canadian bacon and a slice of Swiss cheese on slice of bread, top with second bread slice. Dip each sandwich in egg white/milk mixture, turning to coat both sides.

Melt butter in skillet and pan brown both sides of each sandwich. Top each sandwich with a second slice of Swiss cheese and bake for 15 minutes.

Meanwhile, spray skillet with cooking spray and fry eggs. To serve, top each sandwich with fried egg.