In a small bowl whisk the garlic oil ingredients.
Prepare the grill for direct cooking over medium heat (350° to 450°F) and preheat a perforated grill pan for 10 minutes.
In a large bowl gently toss the onions and bell peppers with 1 tablespoon of the garlic oil. Brush the cut side of the rolls with the remaining garlic oil. Spread the vegetables in a single layer on the grill pan and grill over direct medium heat, with the lid closed, until tender, about 12 minutes, turning occasionally. Remove the grill pan with the vegetables from the grill and put the vegetables into a large bowl. Add the vinegar and stir to coat, separating the onion slices into rings.
Brush the cooking grates clean. Grill the sausages over direct medium heat, with the lid closed, until browned and fully cooked (160°F), 8 to 10 minutes, turning occasionally. During the last 30 seconds to 1 minute of grilling time, toast the rolls, cut side down, over direct heat. Cut the sausages on the diagonal into ½-inch slices. Add the sausages and any juices to the bowl with the onions and peppers.
Top each roll with 1 cup arugula and one quarter of the sausage-onion-pepper mixture. Serve right away.