To Make Onions
- In a medium cast iron pan over medium-high heat, melt butter and oil. Add onions and a pinch of salt; stir to coat.
- Reduce heat to low and cook, stirring every few minutes, until the onions are softened and golden brown, at least 20 minutes.
- Remove from heat, add whiskey, stir to coat, and return to the rangetop. Over medium heat, cook just until the alcohol smell is cooked off; set aside.
To Make Mushrooms
- In a medium cast iron pan over medium-high heat, melt butter and oil. When oil shimmers, add mushrooms, thyme, and garlic; stir to coat in oil, season with salt and pepper, and cook undisturbed at least 5 minutes.
- Stirring occasionally, cook until the mushrooms have released excess water and turn golden brown, about 5 to 10 minutes more. Remove from heat and set aside.
To Make Burgers
- Heat griddle to 375°F. In a large bowl, mix bison and salt until well combined.
- Shape into eight ¼-inch patties; brush with vegetable oil. 3. Cook patties until browned on first side, about 1–2 minutes. Flip and cook to desired doneness, about 1–2 minutes more.
- Serve sliders on buns topped with mayonnaise, mushrooms, onions, and arugula.