Preheat oven to 450 degrees F. Heat a large nonstick skillet over medium-high heat.
Combine meat with salt and pepper, chopped crimini mushrooms, chopped bell pepper, chopped onion, garlic, tomato paste, Worcestershire, crushed red pepper flakes, cheese and parsley. Score and form meat into 4 large patties, 1 inch thick. Drizzle extra-virgin olive oil on top the patties then fry 5 or 6 minutes on each side in a hot skillet.
Place portobello caps on a small baking sheet gill side up and drizzle extra-virgin olive oil on them. Roast the caps 12 minutes. Remove them from the oven and season them with salt and pepper. Turn oven off. Top each cap with about 1/2 cup arugula and a burger. Cap burger with mozzarella and place back in still-warm oven. Melt the cheese 1 minute. Transfer burgers on "bun" bottoms to plates. Top with onions and tomatoes and serve.