Step 1: Prepare the Apples

1. Peel and Slice: Start by peeling, coring, and slicing the apples into thin, even pieces.
2. Mix the Filling: In a mixing bowl, combine the sliced apples with brown sugar, granulated sugar, cinnamon, nutmeg, cloves (if using), and lemon juice. Stir until the apples are well coated.

Step 2: Cook the Apple Filling

1. Heat the Butter: In a skillet over medium heat, melt the butter.
2. Cook the Apples: Add the prepared apple mixture to the skillet. Cook for 5-7 minutes, stirring occasionally, until the apples soften slightly but still hold their shape. Remove from heat and let the filling cool completely.

Step 3: Prepare the Puff Pastry

1. Thaw and Roll Out: If using store-bought puff pastry, ensure it’s thawed. Lightly flour your work surface and gently roll out the pastry sheets to smooth any creases.
2. Cut the Pastry: Use a knife or pizza cutter to divide the pastry into equal squares, rectangles, or circles, depending on your preferred shape.

Step 4: Assemble the Pastries

1. Add the Filling: Place a spoonful of the cooled apple filling in the center of each pastry piece.
2. Seal the Edges: Fold the pastry over the filling (e.g., into a triangle or rectangle). Press the edges with a fork to seal tightly.
3. Add the Egg Wash: Brush the top of each pastry with beaten egg for a golden finish.
4. Sprinkle Sugar (Optional): Sprinkle coarse sugar on top for added crunch and sweetness.

Step 5: Bake the Pastries

1. Preheat the Oven: Set your oven to 400°F (200°C) and line a baking sheet with parchment paper.
2. Bake: Arrange the pastries on the baking sheet, leaving space between each. Bake for 15-20 minutes, or until the pastries are puffed and golden brown.

Step 6: Cool and Serve

1. Cool Slightly: Allow the pastries to cool on a wire rack for 5-10 minutes.
2. Add Toppings (Optional): Dust with powdered sugar or drizzle with caramel sauce.
3. Serve Warm: Pair with a scoop of vanilla ice cream for an extra treat.