Whisk rice vinegar and gochujang in a medium bowl until combined. Stir in soy sauce and toasted sesame oil, then set aside. Alternatively, combine all ingredients in a small jar and shake until emulsified.
Heat oil in a medium nonstick skillet over medium heat. Sauté garlic, ginger, scallion whites, and gochugaru for 60 to 90 seconds until fragrant. Add cabbage, carrot, mushrooms, and kimchi, then cook for 5 to 7 minutes until the cabbage is translucent and reduced.
Transfer the mixture to a bowl and stir in grated tofu, scallion greens, soy sauce, and sesame oil. Mix thoroughly while breaking up the tofu with a spatula. Chill the filling in the refrigerator for 10 minutes if it is too hot to handle.
Prepare a workstation with a bowl of warm water, a wooden cutting board, and a lightly oiled baking sheet. Soften one rice paper sheet in the water for 5 to 10 seconds. Place 3 tablespoons of filling in the center of the paper and fold the sides, top, and bottom inward like an envelope.
Soften a second rice paper sheet and place the dumpling seam-side-down in the center. Wrap it again so the second seam is on the opposite side. Place on the baking sheet and repeat the process for all remaining ingredients.
Heat a thin layer of oil in a nonstick pan over medium-high heat. Pan-fry the dumplings in batches for 2 to 3 minutes per side until lightly browned. Transfer to the baking tray and pat with a paper towel to remove excess oil, ensuring they do not rest directly on the towel.
Coat both sides of the dumplings with oil spray and arrange them in the air fryer basket without touching. Air fry at 375°F for 8 to 10 minutes, flipping halfway through.
Serve the dumplings warm with the prepared dipping sauce. Store leftovers in the refrigerator for up to 3 days and reheat on the stove or in the air fryer to restore crispness.
