Place the ground beef in a bowl. Add Worcestershire sauce, kosher salt, and black pepper. Gently mix with your hands until just combined; avoid overworking. Divide into two equal portions and form each into a patty about 3/4 inch thick, slightly wider than the bun. Make a shallow indentation in the center of each patty with your thumb to reduce puffing while cooking.

Cook patties

Heat a heavy skillet or cast-iron pan over medium-high heat until very hot. Add 1 tablespoon vegetable oil and swirl to coat. Place patties in the pan (do not crowd). Cook 3–4 minutes without moving until a crust forms. Flip and cook another 3 minutes for medium; during the last 1 minute of cooking place a slice of cheddar on each patty and cover the pan to melt the cheese. Internal temperature should reach 160°F (71°C) for well-done or 145°F (63°C) for medium-rare if you prefer less cooked beef.

Remove patties to a plate and tent with foil to rest for 3–5 minutes while you prepare the buns and assemble.

Burgerly Sauce

While patties rest, make the Burgerly Sauce. In a small bowl combine mayonnaise, ketchup, Dijon mustard, sweet pickle relish, apple cider vinegar, paprika, and hot sauce if using. Whisk until smooth and taste; adjust seasoning with a pinch of salt or more vinegar if you want brighter acidity. Refrigerate until ready to assemble.

Buns & Assembly

Toast buns: Spread softened butter evenly on the cut sides of each bun. Place buttered sides down in a clean skillet over medium heat and toast 1–2 minutes until golden and fragrant. Alternatively, toast under a broiler for 1–2 minutes, watching closely to prevent burning.

Assemble burgers: Spread about 1 tablespoon of Burgerly Sauce on the bottom half of each toasted bun. Place a lettuce leaf on the sauce, then a cheese-topped patty. Add two tomato slices, two onion slices, and two pickle slices on top of each patty. Spread a little more sauce on the top bun and close the burger. Serve immediately.

Serve suggestion: Serve with fries, a side salad, or extra sauce for dipping.