Spread about 1 teaspoon mango chutney over each bread slice. Place 1 cheese slice on each of 4 bread slices. Divide turkey evenly over cheese. Top with remaining 4 bread slices, chutney side down. Combine milk and egg in a shallow dish. Dip both sides of each sandwich into milk mixture.
Heat a large nonstick skillet coated with cooking spray over medium heat. Cook sandwiches 3 minutes on each side or until lightly browned.