Cook the bacon: In a skillet over medium heat, cook the bacon until crispy. Transfer to a paper towel-lined plate to drain.
Sauté the onions: Remove excess bacon grease from the skillet, leaving just enough to coat the bottom. Add sliced onions and cook over medium heat for 10–15 minutes, until caramelized. Pour in the Irish stout and simmer until the liquid reduces by half. Season with salt and pepper. Set aside.
Make the patties: In a bowl, mix ground beef with Worcestershire sauce, salt, and pepper. Form into 4 equal patties, shaping slightly larger than the buns.
Cook the burgers: Heat a grill or skillet over medium-high heat. Cook patties for 3–4 minutes per side, or until desired doneness. In the final minute, top each patty with grated cheddar and cover loosely to melt.
Prepare the sauce: In a small bowl, whisk together sour cream, Dijon mustard, and a pinch of salt. Set aside.
Toast the buns: Lightly butter the cut sides of the brioche buns. Toast in a pan until golden brown.
Assemble the burgers: Place a cheesy burger patty on each bottom bun, followed by a scoop of caramelized onions, two slices of bacon, and a generous spoonful of sour cream-Dijon sauce. Top with the upper bun.
Serve: Enjoy immediately with fries or chips—and maybe a cold pint for that full Irish pub vibe.