In a large mixing bowl, combine the ground beef with salt and black pepper. Form the mixture into four equal patties, making a slight indent in the center of each to prevent them from bulging during cooking.

In a saucepan over medium heat, melt the butter and whisk in the flour to create a roux. Gradually add the German lager or ale, whisking continuously until the mixture is smooth. Stir in the shredded cheddar cheese and let it melt completely, keeping it warm.

Slice the pretzel buns in half and butter the cut sides. In a skillet over medium heat, toast the buns until they are golden brown and slightly crispy, about 2-3 minutes.

Preheat your grill or a skillet over medium-high heat. Cook the patties for about 3-4 minutes on each side, ensuring they’re nicely browned. In the last minute of cooking, add slices of Swiss cheese on top to melt.

Place each beef patty on the bottom half of a toasted pretzel bun. Generously drizzle the warm beer cheese sauce over the patties. Top with German pickles, arugula, and thinly sliced red onions before capping with the other half of the bun.

Enjoy the burgers warm, savoring the combination of gooey cheese, juicy beef, and chewy pretzel bun. If the burgers are tall, use skewers to hold them together while serving.