Cook the ground beef in a large skillet over medium heat for about 6–8 minutes, breaking it apart until browned and no pink remains. Drain the excess grease.

Add the diced onion and cook for about 2 minutes until slightly soft. Remove from heat and stir in the shredded cheddar, diced pickles, salt, and pepper. Let the mixture cool to room temperature before filling the wrappers.

Whisk the egg and 1 tablespoon of water in a small bowl to make the egg wash.

Place an egg roll wrapper on a clean surface with a corner facing you. Spoon 3–4 tablespoons of filling onto the lower third. Fold the bottom corner over the filling, fold in the sides, brush the top corner with egg wash, and roll tightly to seal. Repeat with the remaining wrappers.

Heat about 2 inches of canola or vegetable oil in a skillet to 350°F (175°C).

Fry 5–6 egg rolls at a time for about 3–4 minutes per side until golden and crisp. Remove and drain on paper towels, then place on a wire rack to keep them crisp.

Whisk together mayonnaise, ketchup, mustard, relish, minced onion, paprika, vinegar, onion powder, and salt until smooth.

Serve the egg rolls warm with the Big Mac sauce for dipping.