Gently form patties with the ground bison that are slightly larger than the diameter of the buns, as the meat will shrink slightly when cooked.
Heat a cast iron skillet over medium-high heat until it just starts to smoke. Season the patties generously with kosher salt and freshly ground pepper. Add the butter to the skillet, swirl it, then immediately add the patties. Reduce the heat to medium so it doesn't cook too fast.
Cook for about 3 to 4 minutes per side, or until the desired temperature is reached (medium-rare or medium is recommended). Add the sliced cheese about 2 minutes before the burgers are finished cooking to melt.
While the patties rest, toast the buns either in the hot skillet or in the toaster with a thin layer of mayo applied to the inside of the bun.
Serve with sliced onion, tomato, lettuce and whatever you love on your burger. Bison meat is super flavorful, so use minimal sauces so you can really taste it.