Add apples, brown sugar cane, lemon juice, 1 tsp. ground cinnamon and ground cloves to small pot; set pot over medium heat. Cook, stirring occasionally, until sugar dissolves and apples begin to release their liquid. Reduce heat to medium low. Cook, stirring occasionally, until liquid evaporates and apples are tender, about 20-25 minutes. Transfer cooked apples to bowl; chill until cold. (Note: Filling can be stored covered in refrigerator for up to 1 week.)
Heat oven to 425°F. In small bowl, mix sugar with remaining cinnamon until combined; set aside.
On lightly floured work surface, using rolling pin, roll out puff pastry round until about ½” larger in diameter. Spoon 2 tbsp. cooled apple mixture into middle of dough. Moisten edges with beaten eggs; fold in half to form half-moon shape. Seal edges by pressing with fork; transfer to parchment-lined baking sheet. Repeat with remaining pastry rounds and filling to make 12 empanadas. Brush tops of empanadas with beaten eggs; sprinkle with cinnamon sugar. Using tip of knife, make small slit in top of each empanada to vent.
Bake until empanadas are puffed and golden brown, about 20 minutes, rotating pan after 10 minutes for even browning. Transfer empanadas to cooling rack; let sit until cool enough to handle. Serve warm or at room temperature.