Whisk together first 3 ingredients in a shallow dish. Dip both sides of bread in egg mixture.
Melt 1 tablespoon butter in a large nonstick skillet over medium heat; add 3 bread slices, and cook 2 to 3 minutes on each side or until golden brown. Repeat with remaining 1 tablespoon butter and 3 bread slices.
Spread 1 tablespoon strawberry jam on 1 side of each bread slice; top each evenly with turkey, ham, and cheese. Place on a baking sheet.
Broil 5 1/2 inches from heat 2 to 3 minutes or until cheese is melted.