Preheat oven to 400°F (200°C) and line a baking sheet with parchment paper.

In a skillet over medium heat, melt butter. Add diced apples, brown sugar, cinnamon, nutmeg, and lemon juice. Cook for 5–7 minutes until apples are tender and sauce thickens.

Stir in flour and cook for 1 more minute to thicken mixture. Remove from heat and let cool slightly.

Roll out puff pastry sheets and cut each into 4 squares, making 8 total.

Place a spoonful of apple filling in the center of each square. Fold into a triangle and seal the edges with a fork.

Place turnovers on the baking sheet. Brush with beaten egg.

Bake for 18–20 minutes or until golden brown and puffed.

Cool slightly and dust with powdered sugar if desired before serving.