Add sliced mushrooms and cook until golden and moisture evaporates, about 5–7 minutes. Season with salt and pepper. Stir in parsley, if using. Remove from pan and keep warm.
Divide beef into 4 equal portions and gently shape into patties slightly larger than buns. Season both sides with salt and pepper.
Preheat a skillet or grill over medium-high heat. Cook patties for about 4–5 minutes per side for medium doneness, flipping once. Season again mid-cooking, if desired.
About a minute before patties are done, place a slice of Swiss cheese on each so it melts while resting.
If using, spread mayonnaise and Dijon mustard on the cut sides of the toasted buns.