Combine onion, bread crumbs, sweet pepper, catsup, horseradish, mustard, salt, and pepper in a medium bowl. Add ground beef; mix well. Shape meat mixture into eight 3/4-inch-thick patties.

Grill patties on the rack of an uncovered grill directly over medium coals for 14 to 18 minutes or until an instant-read thermometer inserted in side of patty registers 160 degrees F., turning once halfway through cooking. Top each burger with a slice of mozzarella during last 2 minutes of grilling. Remove from grill, sprinkle with basil.

Serve on toasted Italian bread slices or whole wheat buns. Makes 8 servings.

To transport to a picnic site, cover and chill raw meat patties for 1 hour. Transport in an insulated cooler with ice packs. Cook within 1 hour.