Preheat a grill to medium. In a medium bowl, combine 1 tbsp. each sesame oil and water, 1 tsp. hoisin sauce and the garlic. In a small bowl, toss the mushrooms with 1 tbsp. sesame oil; season with salt and pepper. Slice the pork into 4 pieces and brush with the remaining 1 tbsp. sesame oil; season with salt and pepper.
Place the pork and mushrooms on the grill, cover and cook, turning once, until the pork is barely firm and the mushrooms are tender, about 5 minutes. Slice the mushrooms and cut the pork into small cubes; add to the bowl of sesame-hoisin sauce.
Drizzle the EVOO on a baking sheet; turn the dough disks in the oil. Press each disk into a 6-inch round.
Place the dough on the grill, cover and cook until bubbly, about 3 minutes. Flip and brush with the remaining hoisin sauce. Cover and cook until well marked, about 3 minutes.
Meanwhile, add the cabbage and scallions to the mushroom pork mixture. Top the crusts with the mixture.