Preheat a grill or a grill pan to high. Place a double layer of foil, 18 to 20 inches long, on a work surface. In a bowl, combine the peppers, onion and garlic. Liberally drizzle the vegetables with EVOO and season to taste with salt and black pepper. Pile the vegetables on half of the foil, then fold the foil over to cover. Fold up all of the edges to seal, forming a pouch. Place the pouch off to one side of the grill and cook, turning occasionally, for 15 to 20 minutes.
Drizzle the sausages with EVOO and grill, turning frequently, until firm and crisp and the juices run clear, 12 to 20 minutes, depending on the thickness. Let rest for a few minutes, then slice on an angle.
While the sausages grill, in a food processor pulse the giardiniera vegetables with the olives, parsley and lemon zest until the mixture is the consistency of relish.
Fill the rolls with the peppers, onion and sliced hot and sweet sausages; top with the giardiniera-olive relish.