Preheat the oven to 375°F (190°C).
Lightly flour a surface and roll out the dough into a large rectangle, about ¼-inch thick.
Use a knife or pizza cutter to divide it into 4 equal rectangles.
Sprinkle a small amount of shredded cheddar and mozzarella cheese in the center of each rectangle, leaving a ½-inch border.
Spoon the BBQ beef mixture evenly over the cheese, then top with another layer of shredded cheese.
Brush the edges of the dough lightly with water or a beaten egg to help seal.
Carefully fold the dough over the filling, aligning the edges to form a rectangular pocket.
Press the edges together gently, then use a fork to crimp and fully seal the hot pockets.
Transfer the assembled hot pockets onto a parchment-lined baking sheet, spacing them apart for even cooking.