Turn on the oven to 400 degrees. Grease a baking sheet with shortening. Unroll pizza dough on baking sheet. Use a pizza cutter to cut dough into four equal-size squares. Use a table knife to spread 1 tablespoon of the pizza sauce over each square, leaving a 1/4-inch boundary. Place 5 slices of pepperoni on each square. Use the knife to cut each cheese slice in half diagonally. Place cheese on top of pepperoni.
For each pocket, fold the top left corner of the square down over the bottom right corner to make a triangle. With the tines of a fork or with your fingers, press edges of dough together to keep filling inside the pocket.
Use a pastry brush to brush tops of pockets with milk. Sprinkle with Parmesan cheese. Put the baking sheet in the oven. Bake for 15 to 17 minutes or until golden brown. Use hot pads to remove baking sheet from oven. Use pancake turner to remove pockets from baking sheet.