Remove some bread from cut sides of top half of rolls, creating a pocket.
Place in food processor or blender. Pulse to form fine crumbs. Reserve 1/4 cup crumbs for burgers.
Combine ground veal, bread crumbs, basil, egg, 1 Tbsp mustard and black pepper in large bowl, mixing thoroughly. Shape into four 1/2-inch thick patties.
Place patties and bell pepper on oiled grid over medium, ash-covered coals.
Grill veal, uncovered, 10 to 12 minutes, until internal temperature reaches 160 degrees F, turning occasionally. Grill peppers 7 to 11 minutes until tender, turning occasionally. Spread remaining 1 Tbsp mustard on bottom half of rolls. Place rolls, cut sides down on grid. Grill until lightly toasted.
Cut pepper quarters in half lengthwise; place on roll bottoms.