Cook the bacon: In a skillet over medium heat, cook bacon until crispy. Transfer to a paper towel-lined plate. Keep about 1 tablespoon of the bacon fat in the pan.
Caramelize the onions: Add sliced onions to the skillet. Cook slowly over medium-low heat until golden and tender (10–15 minutes). Pour in the Irish stout and simmer until reduced by half — it should be thick and jammy. Season lightly with salt and pepper.
Form and season the patties: In a mixing bowl, combine ground beef, Worcestershire sauce, a pinch of salt, and freshly cracked pepper. Gently shape into 4 patties slightly larger than your buns.
Cook the burgers: Grill or pan-fry over medium-high heat, about 3–4 minutes per side or until cooked to your preferred doneness. In the final minute, top each patty with cheddar cheese and cover to melt.
Make the sauce: In a small bowl, stir together sour cream, Dijon mustard, and a pinch of salt. This tangy sauce balances the burger’s richness.
Toast the buns: Spread butter on the cut sides of the brioche buns and toast in a skillet until golden brown.
Assemble the burgers: Bottom bun → cheeseburger patty → caramelized stout onions → bacon → dollop of mustard-sour cream sauce → top bun.