Finely dice mushrooms or gently pulse in food processor.
In skillet over medium-high heat, warm 1 tablespoon olive oil. Add mushrooms and cook for 5-7 minutes, or until golden brown.
Remove from heat and set aside to cool. Transfer cooled mushrooms to medium bowl.
Add ground beef and salt, mixing until combined. Divide the meat mixture into 4 equal patties.
In the same pan over medium-high heat, add remaining tablespoon of olive oil and cook burger patties until the internal temperature reaches 160 degrees, about 5 minutes per side.
Place cheese slices on top of each patty and cook just until melted.
Remove patties from heat. To assemble, place tomato and onion slices on top of each patty. Top with condiments if desired. Use 2 or 3 lettuce leaves per patty and tightly wrap around each burger.