In a large bowl, combine the flour, salt, and sugar. Add the chilled butter and mix until the mixture resembles coarse crumbs.
Gradually add the ice water, one tablespoon at a time, mixing until the dough comes together. Divide the dough in half, shape into disks, wrap in plastic wrap, and refrigerate for at least 30 minutes.
Preheat the oven to 375°F (190°C). Line a baking sheet with parchment paper.
On a floured surface, roll out one disk of dough to about 1/8-inch thick. Cut into rectangles, approximately 4x6 inches. Repeat with the second disk.
On half of the rectangles, layer the cheddar cheese, breakfast sausage, and scrambled eggs. Sprinkle with black pepper.
Place the remaining rectangles on top of the filled ones and press the edges to seal. Use a fork to crimp the edges and create a decorative pattern.
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 25-30 minutes, or until golden brown. Let cool slightly before serving.