Cook bacon until crispy, set aside on a paper towel to drain.
In a large skillet using the butter over medium heat cook the onion for about 5 minutes sprinkled with the sugar.
Add 3/4 cup beer and continue cooking until onions start to brown and beer is absorbed. Set aside.
In a large bowl using your hand’s mix together the ground beef, red pepper, garlic, 1/4 cup beer, and Dijon mustard.
Form into 4 patties, and sprinkle salt and pepper to taste.
Grill the burgers over medium-high heat and toast the buns on the grill while the burgers are cooking; set the buns aside. (An internal temperature of 155F. seems to work well for me.)
Just before the burgers are done top each one with a slice of cheese, close the grill, and allow the cheese to start to melt. Place the burgers on the buns, top with onion, and stack with the topping.