Prepare the Dried Mushrooms
Begin by processing the dried mushrooms in a food processor or clean coffee grinder until they form a fine powder. Discard any larger, unground pieces, though small fragments can remain.
Mix the Burger Patties
In a large mixing bowl, gently combine the ground beef, kosher salt, black pepper, Worcestershire sauce, and the mushroom powder. Mix the ingredients briefly with your hands, being careful not to overwork the meat, which may lead to a tough texture. Form the mixture into 3 to 4 patties, using about 1/4 to 1/3 pound of meat per patty, and create a slight indentation in the center of each to help them cook evenly.
Prepare the Grill
Set up the grill for high, direct heat. Place a cast iron skillet on the grill grates to heat up simultaneously. Alternatively, heat the skillet on a stovetop over high heat.
Sauté the Mushrooms and Onions
Once the skillet is hot (a drop of water should sizzle upon contact), add the shiitake mushrooms and dry sauté them until they release their moisture, about 2 to 3 minutes. Then, add the sliced onions and olive oil. Toss to combine and continue to sauté over high heat for another minute. Season with kosher salt to taste, cooking until the onions soften and begin to brown. Remove the skillet from heat and set the mushroom-onion mixture aside in a bowl.
Grill the Burgers
Place the patties on the preheated grill and cook to your desired doneness, generally 5 to 8 minutes per side, depending on the patty thickness and grill heat. Near the end of cooking, top each patty with a slice of Swiss cheese, allowing it to melt thoroughly.
Toast the Buns
Lightly brush the hamburger buns with olive oil and toast them on the grill or in the skillet for 1 to 2 minutes, or until golden brown.
Assemble the Burger
Place a cooked burger patty on the toasted bun, then generously top with the sautéed mushrooms and onions. Serve immediately and enjoy this deliciously elevated burger.