Heat a gas grill to high. Drizzle the onions with 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.
nutrition information (per serving):
per main course serving;
Photo: Scott Phillips