In a small bowl, whisk together mayonnaise, sriracha, lemon juice, minced garlic, smoked paprika, and 1/4 teaspoon salt until smooth. Taste and adjust heat or salt as needed. Cover and refrigerate while you prepare the burgers (minimum 15 minutes) to let flavors meld.

Prepare Patties

Form patties

Divide the ground beef into 4 equal portions (about 4 oz each for a 1 lb total). Gently shape each portion into a round patty about 3/4-inch thick, handling the meat minimally to avoid compacting. Make a shallow dimple in the center of each patty with your thumb to reduce bulging during cooking.

Season

Season both sides of each patty evenly with kosher salt and freshly ground black pepper. Lightly brush or rub 1 teaspoon Worcestershire sauce across each patty (split the 1 tsp among patties).

Cook Burgers

Preheat pan or grill

Preheat a cast-iron skillet or grill over medium-high heat until very hot. Add 1 tablespoon vegetable oil to the skillet and swirl to coat (skip oil if using a hot nonstick griddle or well-oiled grill grates).

Sear and cook

Place the patties on the hot surface leaving space between them. Cook undisturbed for about 3 minutes to form a good sear. Flip and cook another 2–3 minutes for medium-rare to medium (adjust time to preference).

Melt cheese

About 1 minute before the patties are done, place a slice of sharp cheddar on each patty. Cover the skillet with a lid or tent loosely with foil to help the cheese melt, about 30–60 seconds.

Prepare Buns & Toppings

Toast buns

While the burgers finish, spread softened butter on the cut sides of the buns. Toast buttered sides down in a separate skillet over medium heat or on the grill for 1–2 minutes until golden and crisp.

Prep toppings

Drain jarred hot cherry peppers and pat lightly with paper towel. Thinly slice any additional peppers if needed. Slice tomatoes and separate lettuce leaves. Have pickle slices ready if using.

Assemble & Serve

Spread about 1 tablespoon of the sriracha aioli on the bottom bun of each burger. Place a lettuce leaf on the aioli, then the cheddar-topped burger patty. Top each patty with about 2 tablespoons (roughly 2 heaping tablespoons) of sliced hot cherry peppers and a few thin red onion slices. Add tomato slice and pickles if using. Spread a little aioli on the top bun and place it on the burger.

Serve immediately while hot. Offer extra sriracha aioli and hot cherry peppers on the side for those who want more heat.