1. Prepare the Secret Sauce: In a small bowl, combine the mayonnaise, ketchup, yellow mustard, minced dill pickle, pickle juice, garlic powder, and smoked paprika. Stir everything together until well combined. Taste and adjust seasoning as needed, then set aside.

2. Form the Meatballs: Divide the ground beef into 8 equal portions. Gently roll each portion into a loose ball, about 2-3 inches in diameter. Do not overwork the meat, as this can make the burgers tough. Place them on a plate and set aside.

3. Toast the Buns: Heat a large cast-iron skillet or griddle over medium heat. Lightly butter the cut sides of the brioche buns. Place the buns cut-side down on the hot skillet and toast for 1-2 minutes, or until golden brown and slightly crispy. Remove and set aside.

4. Heat the Skillet and Smash the Patties: Increase the heat to medium-high. Add a small amount of butter or oil to the hot skillet. Once shimmering, place two or three beef balls onto the skillet, ensuring they are spaced apart. Immediately place a piece of parchment paper over each beef ball, then use a sturdy spatula (or a burger press) to firmly smash each ball down into a thin patty, about 1/4-inch thick. Press down for about 10 seconds to create maximum contact with the hot surface.

5. Cook and Flip the Burgers: Season the smashed patties generously with salt and black pepper. Cook for 2-3 minutes, or until the edges are crispy and browned, and you see juices pooling on top. Carefully scrape the spatula underneath the patty to release it from the skillet, then flip.

6. Melt the Cheese: Immediately place a slice of American cheese on top of each flipped patty. Cook for another 1-2 minutes, or until the cheese is melted and gooey, and the burger is cooked through to your desired doneness.

7. Assemble the Burgers: Remove the cooked patties from the skillet. Spread a generous amount of the secret sauce on both the top and bottom toasted bun halves. Place two cheeseburger patties on the bottom bun, then add any additional desired toppings (like lettuce, tomato, or onion). Top with the other bun half and serve immediately. Repeat with the remaining beef balls.