Preheat oven to 450 degrees.
Combine 1/2 cup pizza sauce, broccoli, cheese, and pepperoni, if using, in a medium bowl.
Flatten each biscuit into a 3-inch round circle, and top half of each with a heaping tablespoon of the broccoli mixture. Fold empty side of biscuit over the mixture. Press the edges with a fork to seal.
Place the pizza pockets on an ungreased baking sheet. Brush each pocket with some of the egg mixture, and pierce a small hole in the top of each one. Bake for 10 minutes, or until golden brown. Serve with remaining pizza sauce.
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