Preheat grill to 300° to 350° (medium) heat. Stir together mayonnaise, vinegar, chili sauce, crushed red pepper, and Italian seasoning. Coat portobello mushrooms with olive oil; sprinkle with kosher salt, pepper, and Greek seasoning. Grill, covered with grill lid, 7 minutes on each side or until tender. Serve on toasted buns with desired toppings.