Add mushrooms to a food processor and pulse until a smooth paste forms, scraping down the sides of the bowl as needed. Transfer the paste to a bowl; do not wash out the processor bowl.
Cook and Drain
Microwave the mushroom paste until it releases liquid and begins to boil, about 3 minutes, stirring halfway through.
Transfer to a fine-mesh strainer set over a bowl. Using a spatula, press the mushrooms to extract ½ cup of liquid and discard. (If more than ½ cup is released, stir the extra liquid back into the mushrooms.) Return the mushrooms to the bowl and refrigerate until cooled to room temperature, about 20 minutes.
Make the Burger Mixture
Return the cooled mushrooms to the food processor. Add the ground beef and salt. Process until the mixture is uniform and starts to pull away from the sides of the bowl, about 20 seconds.
Shape and Season
Divide the mixture into 6 equal portions and shape into patties or balls to make smash burgers.
Patties can be refrigerated overnight or wrapped tightly and frozen for up to 1 month. If frozen, thaw before cooking.
Cook the Burgers
Cook in batches if making all six burgers. Heat oil in a 12-inch skillet over medium-high heat until shimmering. Add the burgers and cook for 30 seconds, then flatten with two offset spatulas. Sprinkle with black pepper if desired. Cook until well browned on one side and flip to other side. Flatten again. Cook second side until browned and the internal temperature reaches 140°F; about 3 minutes per side.
Transfer to a plate and let rest for 5 minutes.
Serve
Garnish with cheese if desired and serve in buns with your favourite toppings.