Heat 1 tsp oil in skillet over medium; thinly slice onion + sauté 8-10 min until browned; season with salt, add 2 tbsp water, cover + cook 3-5 min until softened

Meanwhile, using two packs, wipe 4 mushrooms with a damp paper towel, remove stems + scoop out gills; heat 1 tbsp oil in a skillet over med-high; cook 2-3 min per side until browned + tender; add salt/pep + set aside

Form bison into 2, ¼-inch patties; heat 1 tbsp oil in skillet over med-high, cook with salt/pep 3 min on one side; flip over, cook 2 min + add 2 slices cheese to each; cover + cook 1-2 min until cheese has melted

Divide burgers to mushroom buns + top with caramelized onions