Finely dice mushrooms or gently pulse in food processor.
In skillet, warm 2 tablespoons olive oil on medium-high heat and add mushrooms, sautéing 5-7 minutes, or until golden brown. Remove from heat and cool 5 minutes.
Transfer cooled mushrooms to medium bowl. Add ground beef and salt, mixing until combined. Make 4 patties. Add remaining olive oil to pan and cook burger patties on medium-high heat until desired doneness. Plate and add desired toppings to bun.
Topping recommendations: feta cheese, romesco sauce, sweet peppers and sautéed red onions.