In a sauté pan heat olive oil over medium heat. Add onions, salt and pepper, and 1 tbsp beer. Cook until onions are softened and caramelized. Add the rest of the beer, garlic, sauerkraut, and balsamic vinegar. Cook two (2) minutes more. Remove from heat and let cool.
Combine beef and seasonings until just mixed. Form the mixture into patties and cook in a frying pan until desired doneness is reached.
Mix mustard mayo ingredients together and set aside.
Preheat a sauté pan over medium heat. Butter two slices of rye bread. Lay first slice in pan, spread mustard mayo on slice, add onion mix, beef patty, shredded cheese, then the remaining slice of bread. Toast on one side then flip over until both sides are toasted and cheese is melted. Serve with mayo on the side.