Preheat the air fryer to 200°C (400°F). Add the diced potatoes to a bowl with spray oil and salt, then toss well. Air fry for 20 minutes, shaking halfway, until cooked through with crisp, lightly golden edges. Set aside.
Heat a large pan over medium-high heat and add spray oil. Add the beef mince, season with smoked paprika, garlic powder, onion powder, salt and pepper, and cook until no longer pink, well browned, moisture has cooked off, and it reaches an internal temperature of 71°C (160°F). Transfer the beef to a bowl, leaving the fat and fond in the pan.
Lower the heat to low-medium. Whisk together the whole eggs, egg whites, milk, salt and pepper, then pour into the same pan. Cook gently, stirring slowly, until softly scrambled and just set.
Remove the pan from the heat. Add the cooked beef and air-fried potatoes back into the eggs and gently fold to combine. Stir through the grated cheese while the mixture is still hot so it melts and binds everything together.
Lay out the wraps and divide the filling evenly between them, keeping the filling centred and compact. Roll tightly into firm wraps, folding the sides in first to seal. Wrap each one tightly in foil. Allow to cool completely before refrigerating or freezing.
Chef's Tips
Leave the fat and fond in the pan after removing the beef — cooking the eggs in it straight after adds a real depth of flavour that plain eggs wouldn't have.Fold the cheese through while everything is still hot — this is what melts it into the filling and helps bind the wrap together, rather than leaving separate pockets of cheese.Roll the wraps tightly and fold the sides in first — a loosely rolled wrap is much more likely to fall apart or leak once it's reheated.
Storage & Reheating
Store in the fridge for up to 4 days, or freeze for up to 3 months. Reheat in the microwave for 1-2 minutes from the fridge, or air fry at 180°C (350°F) for 8-10 minutes from frozen for a crispy finish.