Step 1: Prepare the Apple Filling

1. In a medium skillet, melt 2 tablespoons of butter over medium heat.

2. Add the sliced apples and stir occasionally for 2-3 minutes, allowing them to begin softening.

3. Stir in ¼ cup brown sugar, 1 teaspoon cinnamon, ½ teaspoon nutmeg, 1 teaspoon vanilla extract, and 1 tablespoon lemon juice. Let this cook for 5-7 minutes, stirring occasionally until the apples are tender and have absorbed the spices.

4. Mix 1 tablespoon of cornstarch with 1 tablespoon of water, then stir this into the apple mixture. This will thicken the filling and help it bind together.

5. Remove the mixture from the heat and allow it to cool completely before using.

Step 2: Assemble the Puff Pastry Rolls

1. Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.

2. Roll out your puff pastry sheet onto a lightly floured surface, ensuring it’s flat and smooth.

3. Sprinkle a thin layer of granulated sugar over the pastry to create a slightly sweetened crust.

4. Evenly spread the cooled apple mixture over the puff pastry, leaving a ½-inch border on all sides.

5. Carefully roll the pastry from the bottom up, creating a tight log.

6. Slice the rolled pastry into 2-inch pieces, and place the slices cut side up on the prepared baking sheet.

7. Brush the tops of the rolls with the beaten egg wash to ensure a golden finish as they bake.

8. Sprinkle granulated sugar and chopped pecans or walnuts (if using) over the tops for added texture and flavor.

Step 3: Bake & Serve

1. Place the baking sheet in the oven and bake the rolls for 20-25 minutes, or until they are golden brown and flaky.

2. Remove the rolls from the oven and let them cool for a few minutes before serving.