In a medium mixing bowl, combine the Greek yogurt, mayonnaise, diced pickles, mustard, vinegar, garlic powder, paprika, and onion powder. Whisk until smooth and creamy. Cover and place in the refrigerator while preparing the remaining ingredients.
Heat a large skillet over medium-high heat. Add the ground beef and break it apart using a spatula. Sprinkle in the garlic powder, onion powder, paprika, salt, and black pepper. Cook until the beef is browned and fully cooked, stirring occasionally. Drain any excess grease if necessary and set aside for a few minutes to cool slightly.
While the beef is cooking, wash and chop the lettuce, halve the cherry tomatoes, dice the onions, and chop the pickles. Arrange the vegetables in separate bowls or on a cutting board for easy assembly.
Divide the romaine and iceberg lettuce evenly among four serving bowls. Top each bowl with cooked ground beef, cherry tomatoes, diced onions, chopped pickles, and shredded cheddar cheese.
Remove the chilled burger sauce from the refrigerator. Drizzle generously over each bowl or serve on the side for dipping.
Serve immediately while the beef is still warm and the vegetables remain crisp.