Combine the beef, Old Bay and Worcestershire sauce in a medium bowl and mix with your hands. Form into 8 very thin 41/2-inch-wide patties and season lightly with salt and pepper.
Heat 1 tablespoon vegetable oil in a large nonstick skillet over medium-high heat. Add 4 patties and cook until browned, about 2 minutes. Flip, top each patty with a slice of cheese and cook until the cheese starts melting, about 1 minute. Transfer to a large plate and tent with foil; wipe out the skillet. Add the remaining 1 tablespoon vegetable oil and repeat with the remaining patties and cheese.
Meanwhile, toast the English muffins. Combine the Dijonnaise, chopped pickle and brine in a small bowl. Top each English muffin bottom with a lettuce leaf, 2 patties, tomato slices, the Dijonnaise mixture and an English muffin top. Serve with potato chips.