Brown 1 pound ground beef with ½ finely diced onion in a large skillet over medium high heat.
Season with 1 teaspoon salt and ½ teaspoon pepper and cook until the beef is fully browned, about 5–7 minutes. Drain off any excess grease.
In a bowl, mix together 1 cup mayonnaise, ¼ cup French dressing, 2 tablespoons sweet pickle relish, 1 teaspoon white wine vinegar, ½ teaspoon paprika, ¼ teaspoon garlic powder, and ¼ teaspoon onion powder. Stir until well combined.
Add 1 cup of the Big Mac sauce to the ground beef mixture in the skillet and reserve the remaining sauce for serving. Cook for 1–2 minutes until heated through.
To assemble, spread the reserved sauce on the bottom half of each of the 4 hamburger buns with sesame seeds. Top with shredded iceberg lettuce (about 2 cups total), 1 slice American cheese per sandwich, 2–3 pickle slices each, and a scoop of the beef mixture.
Place the top bun on each sandwich and serve warm.