In a large bowl combine beef, Worcestershire sauce, and pepper. On waxed paper shape beef mixture into eight thin 4-inch-diameter patties. Place 1 tablespoon of the blue cheese into the centers of four of the patties. Top with the remaining four patties; pinch edges to seal.
Brush onion slices with olive oil; sprinkle with salt.
Place burgers and onion slices on the rack of an uncovered grill directly over medium-high heat. Grill 5 minutes per side or until done (160 degrees F to 165 degrees F). Brush cut sides of buns with olive oil. Grill, cut side down, the last minute of grilling.
Serve burgers on buns with grilled onion slices, spinach, and remaining cheese.