For remoulade, in a small bowl combine the mayonnaise dressing, cornichons, capers, lemon juice, and black pepper. Cover and refrigerate until ready to serve.
Trim fat from steak. Pat steak dry with paper towels. Using your fingers, rub the garlic spread over steak. Sprinkle with additional freshly ground black pepper. Grill steak and sweet pepper strips on the rack of an uncovered grill directly over medium coalsuntil steak is desired doneness and pepper strips are crisp-tender, turning once halfway through grilling. (For steak, allow 8 to 12 minutes for medium-rare and 12 to 15 minutes for medium doneness.) Cut the steak into 1/4-inch slices.
To assemble, spread the remoulade on the bottom and top halves of rolls. Fill with the arugula, steak slices, and pepper strips.