Peel, core, and dice the apples into small pieces.
Melt the butter in a skillet over medium heat.
Add the apples, granulated sugar, brown sugar, cinnamon, lemon juice, vanilla, and salt.
Cook for 5–7 minutes until the apples begin to soften.
Mix the flour and water together and stir into the apple mixture.
Cook for another 1–2 minutes until slightly thickened.
Remove from the heat and cool the filling completely.
Preheat the oven to 400°F (200°C) and line a baking sheet with parchment paper.
Cut the thawed puff pastry into equal-sized squares.
Place a spoonful of cooled apple filling in the center of each square.
Fold each square diagonally to form a triangle.
Press and crimp the edges with a fork to seal.
Whisk together the egg and water and brush over each turnover.
Sprinkle with granulated sugar if desired.
Cut small vents in the top of each turnover.
Bake for 18–22 minutes, or until puffed and golden brown.
Cool for several minutes.
Whisk together the powdered sugar, milk, and vanilla to make the glaze.
Drizzle the glaze over the turnovers.
Serve warm and enjoy.