Heat skillet over medium-high. Add ground beef and onion.
Cook 6 to 8 minutes, breaking up meat, until browned and onion is soft.
Add garlic, salt, pepper, paprika, and onion powder. Cook 1 minute.
Remove from heat. Drain excess fat.
Stir in cheese, pickles, ketchup, and mustard. Mix until cheese melts.
Cool filling 10 minutes.
Make special sauce. Mix mayonnaise, ketchup, mustard, relish, garlic powder, and paprika. Set aside.
Place wrapper with corner pointing toward you.
Place 2 to 3 tablespoons filling in center.
Fold bottom corner up over filling.
Fold left and right corners to center.
Roll tightly toward top corner.
Brush top corner with beaten egg. Press to seal.
Place seam side down. Repeat with all wrappers.
Preheat air fryer to 390°F for 3 minutes.
Spray basket with cooking spray.
Arrange egg rolls in single layer. Do not let them touch. Work in batches.
Spray tops with cooking spray.
Air fry at 390°F for 10 to 12 minutes. Flip at 5 to 6 minutes.
Remove when golden brown and crispy.
Cool 2 minutes.
Serve hot with special sauce.