Heat the vegetable oil in a large skillet or wok over medium-high heat. Add the garlic and ginger and stir for 30 seconds until fragrant.
Add the shredded cabbage and carrots and stir-fry for 2 to 3 minutes until the vegetables are slightly softened but still have a crunch. Remove from heat and stir in the bean sprouts, green onions, soy sauce, sesame oil, and white pepper. Let the filling cool completely.
Place a spring roll wrapper on a clean surface in a diamond orientation. Spoon about 2 tablespoons of the filling in a line across the lower third of the wrapper.
Fold the bottom corner up over the filling, tuck it in tightly, fold in both side corners, then roll it up firmly like a burrito. Use a dab of water on the top corner to seal it. Repeat with all wrappers.
Preheat the air fryer to 390°F for 2 minutes.
Spray the air fryer basket with cooking spray. Arrange the spring rolls in a single layer, seam side down, leaving space between each one. Spray the tops generously with cooking spray.
Air fry for 8 to 10 minutes, flipping halfway through, until the spring rolls are deep golden brown and crispy all over.
Let the spring rolls cool for 2 minutes before serving, as the filling will be very hot. Serve with sweet chili sauce for dipping.