Prepare the mushrooms: Transfer all of the mushrooms into a strainer and rinse gently with cold water until there is no dirt on the mushrooms. Gently dry the mushrooms with a tea town or paper towel. Set aside.
Heat olive oil in a large skillet pan over medium heat. Add the mushrooms to the pan and season them with salt. Saute the mushrooms for 10-15 minutes, stirring minimally to make sure the mushrooms aren’t sticking to the bottom of the pan.
In the first few minutes of the cooking time, mushrooms will release any moisture they have and that moisture will dissolve or get soaked back into the mushroom. Don’t be tempted to pour it out.
When the moisture is gone and the mushrooms are glossy, remove them from the pan. If you would like crispier mushrooms, turn the heat up to high and saute them for 1-2 additional minutes. Remove the mushrooms from the pan immediately.
Preheat the grill to 450ºF. Lay a piece of tin foil down on the grill.
Prepare the burgers: Add the ground beef, black pepper, and salt to a bowl and gently massage the salt and pepper into the meat. Divide the beef into 4 and roll it into loose balls. Try not to handle the beef too much or it will become tough when cooked.
Add the butter to the tin foil on the grill. When the butter is melted, add the beef balls to the butter and add the sliced white onions to the top of each ball. Gently press the onions into the beef. Allow the beef balls to cook for 2-3 minutes over direct heat.
Use a meat press or a sturdy grilling spatula to press the beef ball into a patty. Press the beef down until it is about ¼ -inch thick, Flip the burger over, and add about ¼ cup of mushrooms, and a slice of Swiss cheese. Grill for an additional 1-2 minutes. Less time for a rare burger.
Remove from the grill and serve on a bun with other burger toppings.