Heat grill. In large bowl, combine all ingredients except cheese, buns and dill dip; mix well. Shape mixture into four 4-inch patties.
When ready to grill, carefully oil grill rack. Place patties on gas grill over medium heat or on charcoal grill 4 to 6 inches from medium coals. Cook 13 to 15 minutes or until thoroughly cooked and no longer pink in center, turning once. Place cheese slice on each patty during last minute of cooking time. If desired, to toast buns, place cut sides down on grill during last 1 to 2 minutes of cooking time.
Spread dip on both cut sides of each bun. Place patties in buns.