Preheat the oven to 275°. Arrange the buns, cut-sides down, directly on the oven rack and bake until warm, about 5 minutes.
Meanwhile, heat a large cast-iron skillet or griddle over medium; coat with cooking spray. Transfer the meat to a large bowl. Using your hands, divide the meat into 4 equal portions and form each portion into a ball. Season the meat generously all over with the kosher salt and pepper, then drizzle with the Worcestershire sauce.
Increase the heat to high, add one portion of meat to the pan, and press down firmly with a spatula to flatten. Repeat with the remaining portions. Cook until the patties are well-browned and crusty around the edges, about 2 minutes. Flip the patties and press; continue cooking about 1 minute more for medium-rare and 2 minutes more for medium-well.
To build the burgers, top each bun bottom with mustard, onion, pickles, lettuce, a burger patty, and 2 generous tablespoons of pub cheese. Add the bun tops.