For the ShackSauce
• ½ cup Hellman's mayonnaise
• 1 tablespoon Dijon mustard
• 1 teaspoon Heinz ketchup
• ¼ teaspoon kosher dill pickle brine
• Pinch cayenne pepper
For the ShackBurgers
• 4 hamburger potato buns
• 4 tablespoons unsalted butter, melted
• 4 pieces green-leaf lettuce
• Eight ¼-inch slices plum tomatoes
• 1 pound cold ground beef, formed into four 1-inch-thick pucks
• Kosher salt and freshly ground pepper, to taste
• 4 slices American cheese
1. Make the ShackSauce: In a small bowl, stir all of the sauce ingredients until smooth, then set aside.
2. Make the ShackBurgers: Heat a large cast-iron skillet over medium-low heat. Meanwhile, open the hamburger buns and brush both sides liberally with the melted butter. Working in 2 batches, place the buns onto the heated skillet, buttered sides down, and cook until golden brown, 2 to 3 minutes. Transfer to a plate and spoon 1 tablespoon of sauce on each top bun, along with a piece of lettuce and 2 slices of tomato.
3. Increase the heat to medium and let the pan heat up for 2 to 3 minutes. On a plate, season both sides of each puck of ground beef with salt and pepper.
4. Place the pucks into the cast-iron skillet, leaving plenty of room between them. Using a large, sturdy metal spatula, firmly smash each puck into a ⅓-inch-thick round patty. Cook the burgers without touching them until the edges are brown and crisp, 2½ minutes, then flip them. Place a slice of American cheese on each burger and continue to cook until medium, 1 minute more.
5. Transfer a cheeseburger to each bottom bun, then sandwich with the top bun and lettuce and tomato and serve.