Cook the ground beef and onion in a large skillet over medium-high heat for 6 to 8 minutes, breaking up the meat, until no pink remains. Drain in a colander for 2 minutes to remove excess fat.
Return the beef to the skillet and stir in the ketchup, mustard, garlic powder and salt. Cook 1 minute, then remove from the heat and let cool for 10 minutes.
Fold the shredded cheddar and chopped pickles into the cooled beef; if the filling is still warm, the cheese will clump instead of staying in distinct shreds, which is what you want.
Lay a wrapper in a diamond shape and spoon 1/4 cup of filling onto the lower third.
Fold the bottom point over the filling, fold in both sides, and roll tightly away from you, brushing the final corner with egg wash to seal.
Repeat with the remaining wrappers, keeping them covered with a damp paper towel so they stay pliable.
Air fry at 380°F: arrange seam side down with space between each roll, spray with oil, and cook 8 minutes. Flip and cook 4 minutes more, until golden and firm when pressed.
Or bake at 400°F on a parchment-lined sheet, brushed with butter, for 14 to 16 minutes, flipping halfway, until the wrapper is deep gold and blistered.
Whisk the mayonnaise, ketchup, relish, vinegar and paprika in a small bowl until smooth; no cooking needed.
Rest the egg rolls 2 minutes before serving with the sauce for dipping.
Good to Know
Swap the cheddar for American cheese slices torn into pieces if that is what is already in the fridge; it melts even softer inside the wrapper.