Brown the ground beef and chopped mushrooms in a large skillet over medium-high heat, breaking up the meat, for 6 to 8 minutes.

Push the mixture to the sides, add onion to the center, and cook 3 to 4 minutes until softened. Stir in garlic for 30 seconds.

Stir in steak sauce, ketchup, Worcestershire, and beef broth. Bring to a bubble, then reduce heat to low and simmer 8 to 10 minutes until thick and glossy. Season with salt and pepper to taste.

Butter the cut sides of the buns, toast in a dry skillet for about 2 minutes until golden, then place provolone on the top buns and broil 1 minute to melt.

Spoon the meat mixture onto bottom buns, top with cheese buns, scatter with crispy fried onions, and serve.