Make the special sauce. Whisk together the mayo, ketchup, mustard, relish, and smoked paprika in a small bowl. Set aside in the fridge.

Form the beef balls. Divide the ground beef into 8 equal portions (about 2 oz each) and roll them loosely into balls. Don't overwork the meat — loose is good here.

Smash the burgers. Heat a large cast iron skillet or griddle over high heat until it's screaming hot. Add a beef ball directly to the dry pan and immediately press it flat with a burger press or the bottom of a heavy spatula. Season generously with salt, pepper, garlic powder, and onion powder. Cook for 2–3 minutes until the edges are deeply browned and crispy.

Add the cheese. Flip each patty, lay a half slice of American cheese on top, and cook for another 1 minute. Remove from heat and set aside. Repeat with remaining beef balls.

Assemble the quesadillas. Lay a tortilla flat on a cutting board. Spread a generous layer of special sauce over half of it. Add a layer of shredded cheddar, then two smash burger patties. Top with pickles, onion, and another pinch of cheddar to help it all stick together. Fold the tortilla in half.

Cook the quesadillas. Melt ½ tablespoon of butter in the same skillet over medium heat. Place the folded quesadilla in the pan and cook for 2–3 minutes per side, pressing gently with a spatula, until golden brown and crispy on both sides. Repeat for all four quesadillas.

Slice and serve. Cut each quesadilla into wedges and top with shredded lettuce, diced tomato, and an extra drizzle of special sauce. Dig in immediately!