Step 1

Preheat the oven to 400 degrees F.

Step 2

Combine the mayonnaise, ketchup, mustard, relish and vinegar in a small bowl; set aside.

Step 3

Working in batches if necessary, add the bacon to a large cast-iron skillet over medium heat. Cook, flipping halfway through, until crisp and golden, about 10 minutes. Transfer the bacon to a nonstick baking sheet. Discard the bacon fat (or save for another use) and wipe the skillet clean but do not wash. Heat over medium-high heat until very hot, about 5 minutes.

Step 4

Add the buns split-side up to the baking sheet with the bacon and bake until the buns are toasted, about 5 minutes.

Step 5

Loosely form the beef into 4 balls. Add one ball of beef to the skillet and press firmly to flatten with a large flat metal spatula for 10 seconds, then gently remove the spatula. Sprinkle the patty generously with salt; repeat with the remaining beef balls, cooking in batches if necessary. Let cook, undisturbed, until well browned on the bottoms, 2 to 3 minutes. Flip the patties, sprinkle with more salt and top each with a slice of Cheddar. Continue cooking until the cheese is melted around the edges and the bottoms are browned, about 2 more minutes.

Step 6

Spread the mayonnaise mixture on the bun tops. Serve the patties on the bottom buns topped with the bacon, onion, tomato and lettuce.