Combine pumpkin, sweetened condensed milk, egg, flour and pumpkin pie spice in a small bowl; mix well.
Add 1 ½ tablespoons pumpkin mixture to the center of one empanada disc. Fold in half and quickly crimp edges with a fork to seal. Place on foil-lined baking sheet. Repeat with remaining empanada discs and pumpkin mixture. Brush empanadas with beaten egg.
Bake at 350° F for 20 to 30 minutes or until golden. Serve warm.