Remove the stick of butter from the freezer and use a cheese grater to grate the frozen butter into a small bowl. Place the butter back in the freezer for a few minutes to re freeze.
In a large bowl, combine the flour, salt, and cocoa powder. Add the frozen, grated butter and mix it into the bowl of flour with a spoon. There will be pea sized balls of butter in the flour.
Add ¼ cup of the ice water to the dry ingredients and start to combine it. Add 1 tablespoon more of water if the dough is still too dry. Use your hands to squeeze the dough together until it forms one dough ball.
Place the dough ball onto a large piece of plastic wrap and flatten it into a disk. Wrap in the plastic and place in the fridge for 30 minutes to an hour to rest.
Once the dough has rested, lightly flour your surface. Unwrap the dough and place it onto the floured surface. Lightly flour the top of the dough. Use a rolling pin to roll the dough out into a large rectangle that is ¼ inch thick. Use a ruller to cut out 3x4 inch rectangles.
Rework the dough scraps into a ball and roll it out again into ¼ thick square and keep cutting out the 3x4 inch rectangles. You will have 8 total rectangles.
Using a pastry brush, lightly brush a bit of the beaten egg onto 4 of the dough rectangles.
Scoop 1 tablespoon of the chocolate fudge filling into the center of the 4 egg brushed rectangles. Lightly press down the filling so that it is flat. Place a second dough rectangle over the fudge filling and lightly press around the edges to seal it in place.
Take a large fork and press straight down into the dough along the edges to further seal them. Carefully transfer the pop tarts to a parchment lined baking tray. Once all the pop tarts are assembled, place the tray in the freezer.
Preheat the oven to 375 F. Once preheated, bake the pop tarts for 20 minutes. Remove and allow to cool competely on a wire rack.