Cook shaved steak in a large pan over medium heat until browned a little. Season with onion powder and garlic powder. Cook until done to your taste, remove from pan, and place in a bowl.
Add onions and pepper to the same pan with the oil from the steak. Season with salt and pepper as desired. Cook until vegetables are softened and onions are almost translucent. Transfer to the bowl with the steak and mix to combine well. Taste and season if needed.
Lay an eggroll wrapper on a work surface diagonally in the shape of a diamond, pat a little oil on each of the 4 corners, and add a packed 1/4 cup steak mixture to the center.
Spread out steak mix in a horizontal line but be careful not to get too close to edges as they will be folded. Take 1/2 slice cheese, fold it in half, and place horizontally on top of steak mix (on top helps the steak stay in place while rolling the eggroll). Dot edges with oil.
To roll the eggroll, first grab the two edges closest to the ends of cheese; fold them over cheese. While keeping fingers in place, fold up the bottom edge of the eggroll wrapper to meet the cheese. Starting from the bottom, roll the eggroll inward making sure it is tight and stuffing stays inside. Repeat with remaining ingredients; this will create 14 to 16 eggrolls.
Set an air fryer to 375 degrees F (190 degrees C), spray eggrolls with cooking spray, and cook for 8 to 10 minutes. Turn eggrolls halfway through cooking time to ensure even browning. Cooking times can vary depending on your air fryer.
Serve with a dipping sauce if desired by combining equal parts mayonnaise and ketchup, dash of Worcestershire sauce, onion powder, garlic powder.
