While the hamburgers are cooking, cook the mushrooms, onions, and butter in a skillet over medium heat until mushrooms are browned and onions have started to caramelize.
Top each hamburger bun with garlic aioli, lettuce, a hamburger, sautéed mushrooms and onions, and bleu cheese crumbles.
Notes
For safe, fully cooked ground beef burgers, aim for an internal temperature of 160℉ (71℃).