Combine mayonnaise, mustard, pickle juice, smoked paprika, garlic powder, and black pepper in a small bowl. Whisk until smooth and refrigerate.
Wash and dry the lettuce. Shred it, halve the tomatoes, and chop the pickles and red onion.
Heat a large skillet over medium-high heat. Add ground beef and cook for approximately 7–9 minutes, breaking it into small pieces until browned and the internal temperature reaches 160°F (71°C).
Drain excess fat if necessary, leaving a little in the skillet.
Reduce heat to medium-low. Add butter and minced garlic. Cook for 30–45 seconds until fragrant.
Stir in smoked paprika, onion powder, black pepper, and salt. Mix thoroughly to coat the beef.
Sprinkle cheddar over the beef, cover the skillet, and cook for 1–2 minutes until melted.
Divide shredded lettuce between four serving bowls. Add equal portions of the garlic butter beef.
Arrange tomatoes, pickles, and red onion over the beef.
Drizzle with the prepared burger sauce and serve immediately.