In a medium bowl, mix together the ground beef, Dijon mustard, Worcestershire sauce, and A-1 steak sauce. Form into 4 patties and set aside.

Heat the olive oil over medium heat in a large saucepan. Add the onions and lightly season with salt. Cook, stirring often, until browned and caramelized ~ about 20 minutes.

Meanwhile, cook the onion rings according to the package.

When there is about 10 minutes left on the caramelizing onions, heat a cast iron pan over medium heat. Add the patties and cook for 5 minutes. Flip and cover for 3 minutes. Remove the lid and finish cooking for 2 minutes for medium doneness.

While the patties cook, make the cheese sauce. Melt the butter in a pot over medium heat. Add the flour and whisk together until thoroughly saturated. Let cook for 1 minute, whisk occasionally. Slowly add in the milk, whisking constantly. Add the sherry cooking wine and gruyere cheese and whisk slowly until melted. Season to taste with salt and pepper.

Place the burger patties on the brioche buns, top with the caramelized onions, onion rings, crispy onions, and gruyere cheese. Serve immediately. Enjoy!