1. Preheat the oven to 425°F. Place the mushrooms and onion on a parchment-lined baking sheet. Drizzle them with 1 tablespoon of the oil, toss to coat, and spread everything out into an even layer. Roast until the mushrooms are deep brown and the onions are soft and charred in spots—25 to 30 minutes.

2. Pulse the roasted veggies in the bowl of a food processor until they are finely chopped but not completely pureed. Transfer the mixture to a medium bowl.

3. To the mushroom and onion mixture, add the egg, salt, rosemary (if desired), garlic powder, and pepper and mix until well combined. Add the beef and mix until all the ingredients just come together, avoiding overmixing. Your hands are the best tool for this job.

4. Next, form the mixture by hand into four patties about ½inch thick (or, six or eight smaller burgers, depending on desired size). Heat the remaining 1 tablespoon oil in a large skillet over medium-high heat, then add the patties and cover the pan. Cook the burgers until the sides facing the pan are well browned—3 to 6 minutes, depending on size. Flip the burgers, then cover the pan and continue cooking for 3 to 6 minutes more. With about 1 minute remaining on the cook time, top each burger with a slice of cheddar if desired. Re-cover the pan and cook until the cheese has melted and the burgers are well browned on both sides and are cooked to medium-rare (145°F) or your desired doneness. Top as desired and enjoy!