In a mixing bowl, combine the flour and salt. Add the cold cubed butter and mix until the mixture resembles coarse crumbs. Gradually add ice water, one tablespoon at a time, mixing until the dough comes together. Form the dough into a disk, wrap in plastic wrap, and refrigerate for at least 30 minutes.

Preheat your oven to 375°F (190°C). Line a baking sheet with parchment paper.

On a floured surface, roll out the chilled dough to about 1/8 inch thick. Cut into rectangles, approximately 3 inches by 4 inches. You should have enough for 8 rectangles (4 tops and 4 bottoms).

In a separate bowl, mix the pumpkin puree, brown sugar, pumpkin pie spice, and vanilla extract until well combined.

Place 4 rectangles on the prepared baking sheet. Spoon about 1 tablespoon of the pumpkin mixture onto the center of each rectangle, leaving a border around the edges.

Place the remaining rectangles on top of the filled ones and press the edges to seal. Use a fork to crimp the edges for a decorative touch.

Brush the tops with the beaten egg. Cut a few small slits in the top of each pop tart to allow steam to escape.

Bake for 20-25 minutes, or until golden brown. Remove from the oven and let cool slightly.

In a small bowl, mix the powdered sugar with milk until smooth to create the icing. Drizzle over the cooled pop tarts.