Caramelize the onions: Heat butter and olive oil in a pan on medium. Add sliced onions, salt, and brown sugar. Cook for 25 to 35 minutes, stirring often, until deeply golden and sticky for tacos.
Make the special sauce: Whisk Greek yogurt with ketchup, pickle relish, Dijon mustard, white vinegar, paprika, garlic powder, salt, and pepper. Taste and adjust seasoning per taste.
Season the beef: In a small bowl, combine ground beef, paprika, garlic powder, onion powder, Worcestershire, salt, and pepper. Divide into 4 equal balls.
Smash and sear: Heat olive oil in a large pan on medium high. Place the tortillas beef side down. Smash with a spatula for the first 30 seconds to get maximum contact. Cook for 3 minutes until the beef forms a deep crust.
Add the cheese: Flip the tacos. Lay a slice of cheddar cheese each one. Cook for 2 minutes until the cheese melts.
Build the tacos: Transfer the tacos to plates beef side up. Pile a spoonful of caramelized onions on top of each. Drizzle the cheese with all pickle slices.
Finish: Drizzle special sauce generously across each taco. Pile shredded lettuce on top. Serve immediately.
