Prepare the Special Sauce
In a small mixing bowl, whisk together mayonnaise, ketchup, mustard, pickle relish, vinegar, garlic powder, onion powder, and paprika. Adjust seasoning to taste and set aside.
Cook the Ground Beef
Heat a large skillet over medium heat. Add ground beef and diced onion. Cook until the beef is browned and the onion is softened, about 7-8 minutes. Drain any excess grease.
Season the beef with salt and pepper. Stir in half of the prepared special sauce and mix well.
Assemble the Sloppy Joes
Reduce heat to low, sprinkle shredded cheddar cheese over the beef mixture, and let it melt. Stir to combine.
Toast the hamburger buns lightly if desired. Scoop the beef mixture onto the bottom half of each bun.
Top with Garnishes
Add diced pickles on top of the beef mixture and drizzle with extra special sauce. Place the top half of the bun on each sandwich.