Preheat the oven to 450 degrees. On a lightly floured work surface, stretch the pizza dough to an 11-by-15-inch rectangle; transfer to a parchment-lined baking sheet.
Spread half the hoisin sauce over the dough, leaving a 1-inch border. Arrange the mushrooms over the sauce, season with salt and pepper and bake until the mushrooms begin to soften, about 10 minutes.
Top the pizza with the pork and cabbage, then sprinkle with the mozzarella. Bake until the crust is golden and the cheese melts, about 8 minutes. Drizzle with the remaining hoisin sauce, then top with the scallions.