In a mixing bowl, combine the flour, sugar, and salt. Add the chilled and diced butter and mix until resembling coarse crumbs.

Gradually add cold water, one tablespoon at a time, until the dough comes together. It should be slightly sticky but not wet.

Form the dough into a disc, wrap it in plastic, and refrigerate for about 15-20 minutes.

While the dough chills, prepare your apple filling by cooking peeled and chopped apples with cinnamon and sugar until tender.

Preheat the oven to 375°F (190°C). Roll out the dough to about 1/4-inch thick on a floured surface and cut into rectangles (approximately 3x4 inches).

Place a spoonful of apple filling in the center of half the rectangles.

Fold the remaining rectangles on top and seal the edges with a fork. Brush with the beaten egg for a golden finish.

Place assembled pop tarts on a baking sheet lined with parchment paper and bake for 20-25 minutes, or until golden brown.

Allow them to cool slightly, then drizzle with powdered sugar icing if desired.