Heat 2 tablespoons neutral oil in a large skillet or wok over medium-high heat. Add the minced garlic and grated ginger and cook for about 30 seconds until fragrant, without browning. Add the shredded green cabbage, purple cabbage (if using), carrots, and chopped mushrooms. Stir-fry for 3–4 minutes until the vegetables start to soften but still have some crunch.

Add the bean sprouts and sliced green onions to the pan. Stir in the soy sauce, rice vinegar, sesame oil, salt, black pepper, and red pepper flakes or chili garlic sauce if using. Cook for another 2–3 minutes, stirring frequently, until the vegetables are tender but not mushy and most of the moisture has cooked off.

Sprinkle the cornstarch evenly over the vegetable mixture and stir well to combine. Cook for 1 minute more to thicken any juices. Transfer the filling to a bowl and let it cool for at least 15 minutes, or chill briefly in the refrigerator. Cool filling helps keep the egg rolls crisp.

On a clean surface, lay out the egg roll wrappers and cover them with a barely damp towel so they don’t dry out. In a small bowl, beat the egg (or prepare water or plant milk for a vegan version). Place one wrapper in front of you like a diamond, with one corner pointing toward you.

Spoon 2–3 tablespoons of cooled filling just below the center of a wrapper. Fold the bottom corner over the filling, tucking it snugly. Fold the left and right corners toward the center like an envelope. Roll up tightly away from you. Brush the top corner lightly with beaten egg, water, or plant milk and press to seal. Repeat with remaining wrappers and filling, keeping rolled egg rolls covered with a towel while you work.

Pour enough oil into a heavy-bottomed pot or deep skillet to reach about 2 inches up the sides. Heat over medium heat until the oil reaches 350°F (175°C). Fry 4–5 egg rolls at a time, without crowding, for 3–4 minutes, turning occasionally, until golden brown and crispy. Transfer to a wire rack set over a baking sheet or a paper towel–lined plate to drain and cool slightly.

Preheat the oven to 400°F (205°C). Line a baking sheet with parchment paper and lightly grease it. Arrange egg rolls seam-side down on the tray. Brush each roll lightly with 2 tablespoons neutral oil or spray with cooking spray. Bake for 18–22 minutes, turning once halfway through, until golden and crisp on the edges.

Preheat the air fryer to 375°F if recommended by your model. Place egg rolls in the basket in a single layer without touching. Spray lightly with cooking spray. Air fry for 8–10 minutes, flipping halfway through, until crisp and golden, watching closely near the end so they don’t over-brown.

Serve the egg rolls warm with your choice of dipping sauces, such as sweet chili sauce, a mix of soy sauce, rice vinegar, and a splash of sesame oil, spicy mayo (mayonnaise mixed with sriracha), or thinned hoisin sauce. Garnish with sliced green onions if desired.