Remove bison steaks from the refrigerator and remove from packaging. Pat steaks dry with paper towels. Season the steaks liberally with kosher salt and black pepper.
Preheat a large 12” metal or cast iron skillet (we do not recommend nonstick for this application) over medium-high heat until very hot. The pan is hot enough when it starts to smoke slightly. Add oil and swirl the pan to coat it with oil evenly. Add bison steaks, cooking on the first side for about two minutes. Do not move or lift the steak during this time, or it will inhibit the sear. Once the steak starts to form a crust on the bottom, flip the steak and cook for another minute until medium-rare.
Turn off the heat. Add 3 tbsp of butter, fresh rosemary, fresh thyme, and smashed garlic cloves to the pan. Tilt the pan, then use a spoon to gather butter and baste it over the steak. Cook the steak to the desired doneness, but because bison is naturally leaner than most other meats, medium-rare is ideal for retaining tenderness.
Remove bison steaks to a cutting board and allow it to rest while making mushrooms. Place the pan back over medium-high heat. The pan should still have leftover butter and browned bits. Add shallots to the pan and cook them for about 1-2 minutes. Add the mushrooms and cook for 3-4 minutes. Next, deglaze the pan with white wine and scrape brown bits from the pan with a wooden spoon. Reduce the wine until it has evaporated, and the pan is almost dry. Add one tablespoon butter and swirl it well to emulsify it into the mushrooms. Season with salt.
Slice steak and place it on a serving platter; arrange mushrooms over the steak. Serve hot.