Heat the grill for high direct grilling. Skewer a few sausages onto each skewer, brush with canola oil and sprinkle with salt and pepper. Grill the sausages until golden brown and slightly charred on both sides, about 5 minutes per side. Remove the sausages to a platter and let rest 5 minutes before removing to a plate.
Toss the tomatoes with the bocconcini, basil, parsley, capers, onions, olive oil and red wine vinegar. Season with salt and pepper and toss to combine.
Slice the bread open and put on the grill, cut-side down, and grill until lightly golden brown. Remove and rub the surface with the garlic cloves, drizzle with olive oil and season with salt and pepper.
Put a whole sausage on each roll and top with the caprese relish. Alternatively, cut the sausage into 2-inch chunks before putting on the rolls.