Heat grapeseed oil in a skillet over medium-high heat. Add onions, sprinkle with salt, and sautée for 10 minutes. Reduce heat to medium, add wine, and sautée another 15 minutes, stirring occasionally until liquid has absorbed and onions are tender. Remove from heat and set aside (can be made a day ahead and chilled).
Combine ground bison, oregano, diced onions, salt, pepper, and garlic powder (if you have any leftover liquid from the sautéed onions, you can add a splash in as well). Divide into four portions and shape into 1/2 inch thick patties. Sprinkle burgers with salt and place on a grill that has been sprayed with non-cook spray or oil, cook until desired doneness (roughly 150°F for medium). Burgers can also be cooked in an oiled large, heavy skillet over high heat, roughly two minutes per side.
Preheat broiler. Open buns and arrange, cut side up, on rimmed baking sheet. Place cheese slices on bun tops. Broil until cheese melts and bottom halves are lightly toasted, about 1 minute. Spread bottom halves with mustard. Top each with a few lettuce or escarole leaves, then the burger. Spoon onions on top of burgers, dividing equally. Cover with bun tops; press lightly.
Serve with french fries and a glass of your favorite medium to full bodied red wine, such as our Il Brigante or Napa Valley Merlot.
Recipe adapted from Epicurious