Shred the green and red cabbage and carrots, slice the green onions, mince the garlic and ginger, and finely chop the mushrooms. Aim for small, slaw-like pieces so the filling cooks quickly and rolls easily.

In a large skillet or wok, heat 2 tablespoons neutral oil over medium-high heat. Add the garlic and ginger and cook, stirring constantly, for about 30 seconds until fragrant, being careful not to burn.

Add the green cabbage, red cabbage, and carrots to the pan. Toss well and cook for 3–4 minutes until the vegetables start to soften but still retain some crunch.

Stir in the mushrooms, bean sprouts, and green onions. Cook for another 3–4 minutes, stirring often, until the mushrooms release their moisture and most of the liquid cooks off. If the pan looks watery, continue cooking until it looks fairly dry.

Add the soy sauce, rice vinegar, toasted sesame oil, kosher salt, black pepper, and crushed red pepper flakes or chili garlic sauce (if using). Cook for 1–2 minutes, stirring to coat the vegetables. Taste and adjust seasoning with a bit more salt or soy sauce if needed.

Sprinkle the cornstarch evenly over the vegetable mixture and stir it in well. Cook for another 1–2 minutes so the cornstarch can absorb excess moisture and slightly thicken the filling. Transfer the mixture to a large bowl and let it cool to room temperature; warm is okay, but not hot, so it doesn’t tear the wrappers.

Place a clean cutting board in front of you. Arrange the egg roll wrappers, the cooled filling, and a small bowl with beaten egg (or a vegan cornstarch slurry, 1 tablespoon cornstarch mixed with 2 tablespoons water). Keep unused wrappers covered with a slightly damp towel so they don’t dry out.

Place one egg roll wrapper on the board with a corner facing you (like a diamond). Spoon about 2 tablespoons of filling slightly below the center. Fold the bottom corner up over the filling, then fold in the left and right corners toward the center. Brush the top corner lightly with egg wash or slurry, then roll tightly toward the top corner, pressing gently to seal. Place the rolled egg roll seam-side down on a tray. Repeat with remaining wrappers and filling.

To fry, heat 2–3 inches of neutral oil in a heavy-bottomed pot or deep skillet to 350°F (175°C). Fry 3–5 egg rolls at a time without crowding the pan for about 3–4 minutes, turning occasionally, until golden brown and crispy. Transfer to a wire rack set over a baking sheet or to a paper towel–lined plate to drain. Adjust heat if they brown too quickly or too slowly.

To bake, preheat the oven to 400°F (200°C). Arrange egg rolls seam-side down on a parchment-lined baking sheet. Lightly brush or spray all sides with neutral oil. Bake for 12–15 minutes, turning once halfway through, until crisp and golden. For extra color, broil for 1–2 minutes at the end, watching closely. Sprinkle with flaky salt if desired.

To air fry, preheat the air fryer to 375°F (190°C). Lightly brush or spray egg rolls with neutral oil and place in a single layer in the basket, leaving space between them. Air fry for 8–10 minutes, turning halfway through, until golden and crunchy. Check around the 7-minute mark and adjust time as needed for your air fryer.

For a quick dipping sauce, stir together 3 tablespoons soy sauce, 1 tablespoon rice vinegar, 1 teaspoon sesame oil, a pinch of sugar, and some sliced green onion in a small bowl.

Let the egg rolls cool for a few minutes, as the filling will be very hot. Serve warm with sweet chili sauce, soy sauce or tamari, hoisin, sriracha or chili crisp, or the quick dipping sauce.