Preheat the oven to 425℉.
Place the flour, baking powder, salt, and yogurt into a large bowl. Using a silicone or wooden spoon, stir until combined. Then, using your hands, press together until a ball has formed.
Transfer the dough to a floured surface. Cut in half and place half back into the bowl. Set aside.
Roll one of the dough halves into a rectangle about 12x8 inches. Cut into 4 squares.
To assemble the hot pocket, evenly distribute pizza sauce, pepperoni, mozzarella, green peppers, and black olives to each square. Pinch to close the open ends.
Place the hot pocket on the baking sheet seam side down. Continue until you have made all of the hot pockets. Then, roll out the second half of the dough and assemble.
Cut a small slit on the top of each hot pocket. Brush the top of each hot pocket with egg wash and sprinkle with cheese and Italian seasoning.
Bake at 425℉ for 10-12 minutes. Remove from the oven and let cool for 5 minutes before serving.*