Combine ground beef and corned beef, mixing lightly but thoroughly.
Lightly shape into six 1/2-inch thick patties. Place patties on grid over medium heat.
Grill burgers covered, but turning occasionally, 7 to 10 minutes until instant-read thermometer inserted horizontally into center registers 160°F.
Evenly top with cheese during last minute of grilling. About 4 minutes before burgers are done, place bread on grid; grill until lightly toasted, turning once.
