Heat olive oil over medium heat in a medium skillet. Add mushrooms and onions. Cook until tender, about 10 minutes, stirring frequently. Add ¾ tsp. salt and ½ tsp. freshly ground black pepper. Keep warm.
Preheat gas or charcoal grill to 400°F. The fire should be quite hot; you should barely be able to hold your hand 3 or 4 inches over the grates. After the coals are gray, spray grates with cooking spray or brush with oil to help keep burgers from sticking. Combine Ground Beef, Worcestershire sauce, ¾ tsp. salt and ½ tsp. black pepper in a large bowl, gently mixing until fully incorporated. Be careful not to over mix. Shape Ground Beef into 8 patties.
Place patties on the grill and cook about 4 minutes per side for rare, and another minute per side for each increasing stage of doneness. Top each burger with Swiss cheese the last 2 minutes of cooking time or until melted.
Place burgers on bottoms of buns. Evenly top burgers with sautéed mushrooms and onions. Drizzle 2 Tbsp. of barbecue sauce on each burger. Top each burger with ¼ cup arugula.