Step 1

In a small mixing bowl, add the ketchup, brown sugar, vinegar, Worcestershire, garlic powder, and onion powder and whisk to combine, before setting it aside.

Step 2

Over medium heat, in a small saucepan, melt the butter. Once the butter has melted, stir in the flour and cook for 1 minute, continuing to stir.

Step 3

Slowly and carefully pour in the milk while whisking constantly. Bring the mixture to a simmer, for 5 minutes before removing it from the heat. Stir in the cheese until melted, and set aside.

Step 4

In a separate large skillet over medium heat, add the beef broth and bring it to a simmer for about 5 minutes.

Step 5

Separate the slices of roast beef, one by one, and drop them into the broth. Adding them individually helps them not stick together, as we don't need to cook the beef, just warm it and flavor it, you only need to let it stay in the broth for 1-2 minutes.

Step 6

Grab an onion hamburger bun and add the homemade sauce from the bowl and spread it on the bun.

Step 7

Top with the roast beef, then add the cheese sauce on top followed by the top of the bun. Serve and enjoy immediately.