In a small saucepan over medium heat, melt the butter until it starts to foam. Gradually add the flour, whisking continuously to create a smooth, paste-like consistency. Continue to cook and stir the mixture until it achieves a light golden brown color, approximately 5 minutes.
Slowly pour in the beef broth, whisking vigorously to prevent any lumps from forming. Allow the mixture to simmer and thicken for about 2 minutes, ensuring a smooth texture. Incorporate the ketchup, Dijon mustard, Worcestershire sauce, onion powder, garlic powder, salt, and ground black pepper into the mixture.
Continue to cook the gravy, whisking frequently, until it thickens to your desired consistency, about 5 more minutes. Adjust seasoning as necessary, and serve hot.