In a large skillet, cook mushrooms in hot oil over medium heat until tender, stirring occasionally. Sprinkle with salt and pepper. Stir in vinegar. Cook, uncovered, until all of the vinegar is evaporated, stirring occasionally.
For a charcoal grill, grill pre-baked pizza crust on the rack of an uncovered grill directly over medium coals about 3 minutes or until bottom is lightly browned. (For a gas grill, preheat grill. Reduce heat to medium. Place pre-baked pizza crust on grill rack over heat. Cover and grill as above.) Remove from grill.
Spread cooked mushrooms over browned side of pizza crust. Sprinkle with cheese. Return pizza crust to grill. Cover and grill for 2 to 3 minutes more or until bottom is lightly browned and topping is heated through. Sprinkle with marjoram. Cut into wedges.