Make the burger sauce by combining the mayonnaise, ketchup, spicy brown mustard, minced pickles, pickle juice and paprika in a small bowl. Season to taste with salt and freshly ground black pepper and refrigerate until you are ready to use it.
Divide the meat in half and season with salt and pepper by sprinkling on all sides of the meat.
Spread some butter on the open sides of the buns. Heat a cast iron or heavy skillet over medium heat. Place the buns, cut side down in the pan and toast until golden brown.
Turn the heat up to medium-high. Place the ground beef balls in the pan and firmly press down with a metal spatula or bacon press for 10 seconds. Cook for 3 minutes until the meat has browned, is a little crispy on the edges and you start to see juices on the top of the burger. Flip the burger over and cook for another minute or two. Top the burgers with cheese (if using) and cook for another two minutes.
Spread some of the special sauce on the bottom of the burger buns. Add some shredded lettuce, a slice of tomato and the burger patty. Spoon some more special sauce on top of the burger and finish with the top of the bun. Serve immediately with lots of napkins!