In a large bowl, whisk together the flour, sugar, and salt. Cut the butter into the mixture until it resembles a coarse meal. Drizzle the ice water over the mixture, stirring until large clumps form.

Transfer the dough to a floured surface and bring it together into a ball. Flatten each half into 1-inch-thick discs, wrap tightly in plastic wrap, and refrigerate for at least 2 hours.

Roll out one disc into a 9×12-inch rectangle, about 1/8 inch thick. Cut into 9 rectangles (3×4 inches) and place on a lined baking sheet. Repeat with the second disc.

For the filling, mix brown sugar, cinnamon, and flour in a small bowl.

Brush egg wash over the surface of each bottom rectangle. Place a heaping tablespoon of the filling in the center of each and spread it around, leaving a 1/4-inch border.

Brush egg wash on each top rectangle, then place them, egg-wash-side-down, on the filling-topped bottoms. Press around the filling to seal.

Poke 6 to 8 holes in the tops of each filled pastry for steam to escape. Crimp the edges with a fork and refrigerate uncovered for at least 20 minutes.

Preheat the oven to 350°F (177°C). Brush the tops with egg wash and bake for 25–30 minutes until golden brown.

Let cool on the pan for 5 minutes before transferring to a cooling rack.

For the icing, whisk together the confectioners’ sugar, milk, cinnamon, and vanilla until thick but spreadable.

Spoon the icing on top of each cooled pop tart and spread. Allow the icing to set for about 1 hour.