Whirl bread in a food processor or blender until fine crumbs form. Pour crumbs into a bowl and combine with minced tomatoes and 6 tablespoons of the reserved oil, eggs, salt and pepper. Add ground beef and gently mix with a fork just until ingredients are evenly blended.
Divide meat mixture into 24 equal portions, each a generous 1/2 cup. With your hands, shape each portion into a 4-inch wide patty. In the center of 12 of the patties, gently make a shallow depression about 2-inches wide; place about 2 tablespoons of the fontina cheese in each depression. Gently top each cheese-topped patty with a plain patty; press edges together to seal well. Lay patties side by side on 2 platters. Cover airtight and chill at least 20 minutes or up to 24 hours.
Prepare a gas or charcoal grill for direct, high heat (you can hold your hand 1 to 2 inches above the cooking grate only 2 to 3 seconds; visit www.safeway.com's Grilling Essential section for complete instructions). Place patties on oiled grill; cover gas grill. Cook 6 minutes, then turn burgers with a wide spatula. Continue cooking until meat is no longer pink in center (make a small cut to test, but be careful not to let cheese drip out), about 7 minutes longer. Transfer burgers to a platter and loosely drape with foil. Place buns with cut sides down and grill and cook until toasted, about 1 minute. Lift buns to a second platter.
Tuck burgers inside buns and garnish to taste.