Combine beef, Worcestershire sauce, garlic, oregano, parsley, salt and pepper in a mixing bowl with your hands. Chill to combine flavors.
While meat chills, heat olive oil, 2 turns of the pan, over medium-high heat. Add onions, season with salt and pepper and let sweat 5 minutes. Add peppers and chili pepper, and cook 7-8 minutes more to soften. Keep onions and peppers moist and saucy with stock.
Bring meat to room temperature and form 6-8 patties that are thinner at the center than the edges for even cooking. Drizzle patties with olive oil to coat and cook over medium-high heat on a hot grill or griddle pan to desired doneness, about 8 minutes, turning once for pink center. Melt 2 slices of provolone over each patty in last minute of cooking time. Serve burgers on toasted crusty rolls and top with saucy peppers and onions.