Combine the flour and salt in a large mixing bowl. Cut the butter and shortening into the flour mixture until coarse crumbs form.

Toss in enough ice water to moisten the flour until the mixture holds together. Shape the dough into equal size discs, wrap in plastic wrap, and refrigerate for at least 2 hours.

Roll one chilled disc into a 9×12 inch rectangle that is ⅛ of an inch thick. Cut the rectangle lengthwise into 3 strips and then cut each strip into thirds to make 9 small rectangles.

Place the rectangles on a parchment-lined baking sheet and refrigerate. Repeat with the second disc.

Preheat the oven to 350°F. Mix the pumpkin puree, brown sugar, and pumpkin pie spice in a small bowl. Set aside.

Divide the filling evenly among the 9 rectangles, placing it in the center of each pastry.

Whisk the egg and milk together. Brush the egg wash on the outer edges of the pastry around the filling.

Remove the second set of rectangles from the refrigerator and brush the entire surface with egg wash. Place each rectangle over the filling, press to seal, and brush the tops lightly with egg wash. Cut small slits in the top to allow steam to escape.

Bake for 25 to 30 minutes, until light golden brown. Rotate the pan halfway through baking.

Cool the pop-tarts on the pan for 10 minutes, then transfer to a cooling rack.

For the icing, whisk all ingredients together until smooth. Spread icing over the cooled pop-tarts.