Form beef into four 3-inch-diameter patties Form cheese into two 1-1/2-inch rounds; place cheese atop two beef patties. Top each with another beef patty, sealing at edges. Season with pepper.
Prepare barbecue (medium-high heat) or preheat broiler. Brush barbecue rack with vegetable oil. Grill burgers until charred outside but still juicy, about 3 minutes per side. Grill bread slices until lightly toasted, about 1 minute per side. Place each burger on 1 bread slice.
Top with tomato, onion, arugula and another bread slice and serve.
Servings: