In a large bowl combine ground beef, garlic, red pepper, ¼ cup beer, Dijon mustard, salt, and pepper.
Mix until well combined. Form mixture into 4 patties that are 1” thick. Grill on medium heat for 4-6 minutes per side.
While burgers are cooking, to make beer braised onions- Melt butter in a large skillet.
Add onions and cook while stirring over medium heat for 5-6 minutes or until tender. Add a ¾ cup of beer and 1 tablespoon of sugar. Cook until the beer is absorbed and the onions are lightly browned (about 15 minutes).
Just before burgers are done cooking top each burger with shredded cheese and heat until slightly melted. Remove burgers from the grill. Serve on toasted buns and top with onions.