Cover beans with water in a saucepan. Bring to a boil, then reduce heat and let simmer until easily mashed with a fork, about 20 minutes. Drain and let cool in a large bowl.

Meanwhile, saute onion, mushrooms, and garlic together in a shallow pan until softened. Remove from heat and set aside.

Mash beans with a fork or potato masher, leaving slightly chunky. Stir in onion mixture. Mix in sauce and beaten egg. Use a small measuring cup to form patties - add breadcrumbs or more sauce as needed to get a moldable patty.

Heat saute pan with a small amount of oil over medium. Once oil is shimmering, drop patties from measuring cup into pan and slightly press them down to create a flat burger.

Cook for approximately 5-7 minutes on each side.