Prepare your grill for high, direct heat. While the grill is heating up, heat a large sauté pan over high heat for 1 minute. Add the mushrooms and dry-sauté them until they release their water, about 2-3 minutes.
Add the onions and the olive oil, toss to combine and continue to sauté over high heat 1 minute. Add salt to taste and cook until the onions soften and begin to brown. Turn off the heat and place in a bowl.
Grill the burgers to the desired doneness, between 5-8 minutes per side, depending on the thickness of the burgers and how hot your grill is.
When the burgers are almost done, lay the Swiss cheese over them and allow the cheese to melt. Paint the burger buns with a little olive oil and toast them on the griddle or grill grates. To assemble, put a burger on the bun and top with the sauteed onions and mushroom mixture.