Sprinkle your rolling surface with a handful of flour or cornmeal. Place dough directly in the middle of the surface. Roll dough out gently 1/4-inch thick, into either a 12-inch rectangle or circle. Brush both sides with olive oil and set aside until ready to grill.
Place dough in the center of the cooking grate, directly over the heat for one to three minutes, until the crust is well marked and browned. Flip dough and spread hoisin sauce evenly over cooked side of crust. Spread chicken, scallions, cilantro, and bell pepper evenly over crust. Sprinkle cheese over the top. Move to Indirect heat (for charcoal: the side of charcoal grill that has no coals. For gas: turn off burner directly under pizza). Cover grill and cook for 5 to 10 minutes, or until bottom is well browned, and cheese is fully melted.
Remove from grill, season with salt and pepper, and slice. Serve immediately.