Add all of the ingredients for the bison burger patties to a large mixing bowl. Use your hands to mix everything together until well combined.
Place a cast iron or non-stick skillet on your stove top. Add enough oil to generously coat the surface and heat to medium-high.
While the skillet is heating, form burger patties. Divide the meat into two to four portions - for 1/2-pound burgers, divide the meat in half, for 1/3-pound burgers, divide the meat into thirds, etc. Form a ball out of one portion of the meat. Press the meat into a disc, making sure it has uniform thickness throughout so that it cooks evenly.
Repeat for the remaining meat, and place patties on a plate while skillet continues to heat the rest of the way. Note: During the cooking process, the center of the burgers will bow out and become thicker in the center. To avoid this, press the center of the patties down so that they appear lower than the sides of the patty.
Test the skillet by carefully flicking water onto the surface. If the oil sizzles and pops, it is ready for cooking.
Carefully place the burger patties on the hot skillet, giving them at least 1 inch of space between for even cooking. Note: To avoid fat and oil splatter, place a fine mesh splatter screen over the skillet.
Cook 3 minutes, or until the first side is browned and crispy. Carefully flip and cook another 3 minutes. Continue cooking and flipping every one to two minutes, until burgers reach desired doneness. For medium-rare burgers, cook burgers a total of 6 minutes. For medium, 7 to 8, and for well-done burgers, 9 to 10 minutes total.
Add the cheese after you've finished flipping the meat. Cover the pan with a lid until cheese has melted.
Transfer the burgers to a plate or cutting board and allow them to sit 2 to 5 minutes before serving. This allows the juices to distribute throughout the meat and collect on the plate rather than causing the bun to get soggy.
Serve burgers on toasted buns along with your favorite toppings, such as tomatoes, red onion, mixed greens, avocado, and pesto sauce.