Whisk together the mayonnaise, ketchup, mustard, diced pickles, pickle brine, and smoked paprika in a small bowl until well combined. Set the sauce aside. While you're prepping, tear or chop the lettuce into bite-sized pieces, dice the tomatoes, and slice the pickles into spears or chips. Having everything ready before you start cooking the burgers will keep you organized once the high-heat cooking begins.

Preheat your oven to 400°F. Line a baking sheet with parchment paper and create 12 small piles of freshly shredded cheddar cheese, spacing them about 2 inches apart (this allows them to crisp evenly). Bake for 8-10 minutes until the edges are golden brown and lacy. Remove from the oven and let the cheese crisps cool on the baking sheet for 2-3 minutes so they firm up, then transfer to a plate. I find freshly shredded cheese works much better than pre-shredded because it melts more evenly and gets crispier.

While the cheese crisps cool, divide the ground beef into 12 equal portions and loosely form each into a ball (don't pack them tightly). Heat a cast-iron skillet or heavy-bottomed pan over medium-high heat until it just begins to smoke, about 2-3 minutes. Working in two batches, place 6 beef balls in the hot skillet and immediately flatten them with a spatula into thin patties, pressing firmly for 2-3 seconds to create a nice crust. Season generously with salt and pepper right after flattening, then cook undisturbed for 1-2 minutes until a golden brown crust forms. Flip each patty and cook for another 30-60 seconds on the second side. Transfer to a plate and repeat with the remaining 6 beef balls. The key to a great smash burger is getting that skillet screaming hot and pressing down hard to maximize the contact between meat and pan for maximum crust development.

Divide the prepared lettuce among your serving plates, creating a bed for each salad. Scatter the diced tomatoes and pickles over the lettuce. Arrange 6 of the cooked smash burgers from Step 3 on each plate, breaking them into pieces or leaving them whole depending on your preference. Top the burgers with the cooled cheese crisps from Step 2, drizzle generously with the special sauce from Step 1, and serve immediately while the burgers are still warm.