In a bowl, mix the ground beef with the other ground beef. Add mustard, garlic powder, salt, and pepper to the meat and combine well. Form four patties, ensuring they are evenly shaped for even cooking.

Slice the white onion into strips. Cook in a skillet over medium heat until tender, about 5-7 minutes. Stir occasionally to prevent burning.

For the Beer Cheese, melt butter in a medium saucepan over medium heat. Add flour and whisk until a paste forms, about 1-2 minutes.

Whisk in the milk and stir for about a minute until smooth. Gradually whisk in the Worcestershire sauce, mustard, garlic powder, paprika, and salt. Stir in the cheddar cheese until melted and smooth. Remove from heat and let it thicken for a few minutes.

To assemble the burgers, take a pretzel bun, place a beef patty on it, add the desired amount of beer cheese, and top with the cooked onions. Enjoy your delicious dinner!