Place bread crumbs in milk to soften. Stir together honey, soy sauce and water until thoroughly combined.
To ground beef, add bread crumbs, soy mixture, onions, garlic, and ginger. Using your hands, mix just until ingredients are incorporated. Do not over mix. Too much handling of the meat can cause it to be tough. Shape meat into six 3/4 inch patties. Set aside.
Rinse mushrooms well. Dry with a paper towel and slice. Saute the mushrooms in 1 teaspoon of butter. Cook until all liquid is absorbed.
Preheat your gas grill or light your coals. Coals are ready when they are covered with grey-white ash. With a paper towel dampened with canola oil, liberally coat grill before setting on barbecue.
Place burgers on grill. Cook uncovered for 15 to 18 minutes, or until instant-read thermometer inserted in center of burger registers 160 degrees, turning burgers once during cooking. About 1 or 2 minutes prior to removing the burgers from the grill, place 1 slice of cheese on top of each burger. When cheese begins to melt, remove burgers to the toasted buns. Top each burger with a teaspoon of sauteed mushrooms and some crisp bacon.