Remove some bread from cut sides of top half of rolls, creating a pocket and place in food processor or blender container. Cover; pulse on and off, to form fine crumbs. Reserve 1/4 cup crumbs for burgers.
Combine ground veal, 1/4 cup bread crumbs, basil, egg, 1 tablespoon mustard and black pepper in large bowl, mixing lightly but thoroughly. Shape into four 1/2-inch thick patties.
Place patties in center of oiled grid over medium, ash-covered coals; arrange peppers around veal. Grill veal, uncovered, 10 to 12 minutes, until instant-read thermometer inserted horizontally into center registers 160°F, turning occasionally. Grill peppers 7 to 11 minutes or until tender, turning occasionally. Meanwhile, spread remaining 1 tablespoon mustard on cut sides of bottom half of rolls. During last 1 to 2 minutes of grilling, place rolls, cut sides down, on grid. Grill until rolls are lightly toasted.
Cut peppers quarters in half lengthwise; place on roll bottoms. Top with burgers. Close sandwiches.
Cook’s Tip: Discard or reserve remaining bread crumbs for other use. Crumbs may be frozen, tightly covered, up to 3 months.