01 -
In a small mixing bowl, whisk together ketchup, light brown sugar, apple cider vinegar, Worcestershire sauce, garlic powder, and onion powder until the mixture is smooth. Set aside to allow the flavors to meld.
02 -
Melt the unsalted butter over medium heat in a small saucepan. Add all-purpose flour and cook for one minute, stirring constantly until a foamy paste forms. Gradually pour in the whole milk while whisking, then bring the mixture to a steady simmer. Stir frequently for approximately five minutes until thickened. Remove from heat and whisk in the sharp cheddar cheese until completely melted and the sauce is silky smooth.
03 -
Pour beef broth into a large skillet and bring to a simmer over medium heat for five minutes. Gently separate the sliced roast beef and add it to the warm broth in batches. Heat each batch for one to two minutes, ensuring the beef is thoroughly warmed, then transfer to a plate using tongs to drain excess liquid.
04 -
Spread a generous spoonful of Arby's sauce onto the bottom half of each onion hamburger bun. Layer warmed roast beef evenly on each bun, then drizzle with cheddar cheese sauce. Cap with the top half of the bun and serve immediately, while the sandwiches are hot and the cheese is melted.