Stir mayonnaise, relish, onion, mustard, ketchup, vinegar, and onion powder together in a small bowl. Season with paprika and salt; set aside.
Cook and stir ground beef in a nonstick skillet until browned and crumbly, about 5 minutes; set aside.
Slice off the side of each pickle and hollow out the core of pickle with a spoon to create a space to fill; set aside.
To assemble, add tomato, onion, pickles, ground beef, and cheese to a board. Drizzle with burger sauce, then chop all ingredients together. Scoop up a small amount of mixture and fill each pickle. Drizzle with more burger sauce and enjoy. Refrigerate any extra sauce in a jar with a lid for up to 2 weeks.
