Make the sauce: In a bowl, whisk together chicken broth, steak sauce, and Dijon mustard. Set aside.
Brown the beef: In a large skillet over medium-high heat, cook ground beef for 7–8 minutes, breaking it up as it cooks. Drain the fat and remove from the pan.
Cook the veggies: In the same skillet, melt butter. Add mushrooms, chopped onions, and Montreal steak seasoning. Cook for 7–8 minutes until mushrooms brown and onions soften.
Add the flour: Sprinkle flour over the veggies. Stir and cook for 1–2 minutes until the flour turns golden and smells nutty.
Simmer with sauce: Return beef to the pan. Pour in the broth mixture and stir. Simmer for 3–4 minutes until the sauce thickens.
Assemble and serve: Spoon ⅓ cup of the mixture onto each toasted bun bottom. Add 1 tablespoon of shredded Cheddar. Top with the bun and serve warm.
