Heat the butter and olive oil in a large skillet over medium heat.
Add the chopped onions and cook until they become translucent (about 2-3 minutes).
Add the sliced mushrooms and cook until they release their moisture and start to brown (about 5-7 minutes).
Stir in the minced garlic and cook for an additional minute.
If desired, deglaze the pan with beef broth or white wine and cook until the liquid evaporates. Season with salt and pepper to taste.
3. Cook the Burger Patties
Heat a grill or skillet over medium-high heat.
Cook the burger patties for about 4-5 minutes per side, or until they reach your desired level of doneness. During the last minute of cooking, place a slice of Swiss cheese on each patty and cover the skillet to melt the cheese.
4. Assemble the Burgers:
Toast the hamburger buns if desired.
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