Set your oven to 375°F (190°C) and line a baking sheet with parchment paper.
Spread the tortillas out flat and place roast beef and shredded cheese in the center of each, leaving space at the edges.
Roll each tortilla up tightly, then place them seam-side down on the prepared baking sheet.
Using a pastry brush, coat the tops with melted butter and sprinkle evenly with garlic powder, onion powder, and dried parsley.
Bake in the oven for about 12 to 15 minutes, until the tortillas are golden and the cheese inside has melted.
While the roll ups are baking, make the au jus by combining beef broth, Worcestershire sauce, soy sauce, onion powder, garlic powder, salt, and pepper in a saucepan and simmering for 5 to 7 minutes.
Once baked, slice the roll ups into 2 to 3 inch pieces and serve warm, accompanied by the au jus for dipping.