Preparation

• 热气体烤架高。细雨的洋葱1 Tbs. oil and 1 Tbs. vinegar and season well with salt and pepper. Toss gently to keep the disks intact. Season the tomato slices with salt and pepper and drizzle with 1 Tbs. oil. Brush 2 Tbs. of the oil over both sides of the bread, rub with the smashed garlic, and season with salt and pepper.
• Put the sausages and onions on the hottest part of the grill. Grill the onions, turning them a few times, until they’re browned and have softened to a limp texture, about 8 minutes. Grill the sausages, turning occasionally, until fully cooked (160°F on an instant-read thermometer), 10 to 12 minutes. Remove the sausages and let them rest. Grill the bread for 1 to 2 minutes on each side.
• Dress the arugula with the remaining 1 Tbs. oil and 1 tsp. vinegar; season with salt and pepper. Arrange a small handful of the arugula and 1 or 2 slices of tomato over four of the bread slices. Slice the sausages in half lengthwise and lay them flat over the tomatoes. Lay a generous portion of the grilled onion rings and a sprinkling of Parmigiano over the sausages. Top with the remaining four slices of bread. Slice the sandwiches in half and serve.