Char the poblanos all over under a hot broiler or over an open flame. Place in a bowl, cover and let cool. Discard the seeds and thinly slice.
Preheat the oven to 375 degrees. Arrange the bacon on a broiler pan and bake until crisp, 15 to 17 minutes.
Meanwhile, heat 1 1/2 tablespoons butter in a skillet over medium heat. Add the onion and cook until lightly browned, about 10 minutes; season with salt and pepper. Transfer to a bowl. Return the pan to medium-high heat.
Season the beef with the worcestershire, salt and pepper. Form 4 very thin patties to fit the shape of your bread. Add a drizzle of oil to the hot skillet, then add the patties and cook through, turning once, 6 to 8 minutes.
Wipe out the pan and return to medium heat. Add another drizzle of oil, then the eggs; cook, over, to soft or medium. Transfer to a plate.
Scantly butter the bread on one side. Place 4 bread slices buttered side down and top each with a few slices of poblano, 2 cheese slices, a beef patty, some bacon, an egg, 2 more cheese slices, some onions and the remaining bread slice, buttered side up. Grill the sandwiches on medium heat, turning once, until deep golden, about 5 minutes.