For the Stuffed French Toast, mix cream cheese, brown sugar and nutmeg in small bowl until well blended. Spread 2 tablespoons of cream cheese mixture on each of 8 slices of bread. Top each with second bread slice to form 8 sandwiches.
Beat eggs with wire whisk in 13x9-inch baking dish. Stir in milk, vanilla and rum flavor until well blended. Dip sandwiches in egg mixture, soaking for 2 minutes on each side.
Melt 1 tablespoon of the butter in large nonstick skillet or griddle on medium-low heat. Place 4 of the sandwiches in skillet. Cook 4 to 5 minutes per side or until golden brown. Repeat with remaining sandwiches, melting remaining tablespoon butter in skillet.
Meanwhile, for the Spiced Syrup, mix pancake syrup, vanilla and pumpkin pie spice in microwavable bowl or measuring cup. Microwave on HIGH 1 minute or until warm, stirring once. Serve with French toast.