Dipping Sauce: Add the rice vinegar and gochujang to a medium bowl and whisk until evenly combined. Add the soy sauce and toasted sesame oil to a medium bowland briefly mix again; set aside. Note: you can also add all ingredients to a small jar and shake well until emulsified.
Cook the Filling: Warm the oil in a medium nonstick skillet over medium heat. Add the garlic, ginger, white portions of the scallion, and gochugaru (if using). Sauté for 60 to 90 seconds, until the garlic is fragrant but before it starts to brown. Add the cabbage, carrot, mushrooms, and chopped kimchi to the pan; cook for 5 to 7 minutes, stirring occasionally, until the cabbage has reduced in size and is translucent.
Mix: Remove the pan from the heat and transfer to a bowl. Add in the grated tofu, remaining green portions of the green onions, soy sauce, and sesame oil. Mix well until combined, using a spatula to break up the tofu some. The tofu should cool the mixture down, but if it’s too hot to handle you can also place it in the fridge for about 10 minutes. This filling can be prepared in the fridge up to 3 days in advance (just store in the refrigerator in the meantime).
Wrap: Fill a large bowl with warm water and set a wooden cutting board and nonstick baking sheet lightly sprayed with oil at your work station. Soak one sheet of rice paper in the water for 5 to 10 seconds, until it softens. Place the rice paper on the cutting board and put 3 tablespoons of the dumpling filling in the center of the sheet. Fold the two sides of the wrapper into the center, then fold the top and bottom sides to the center as well, sort of like you are folding an envelope. (Note: see blog post photos and video for more direction)
Wrap Again: Soften another sheet of rice paper, then place the wrapped dumpling seam-side-down into the center of the second sheet. Wrap again so that the seam for the second sheet is on the opposite side. Transfer to the baking sheet. Repeat steps 4 and 5 with the remaining rice paper wrappers and filling until used up.
Pan Fry: Add enough oil to the bottom of a nonstick pan so it creates a thin and even layer. Warm the oil over medium-high heat. Working in batches, pan fry the dumplings for 2 to 3 minutes on each side until lightly browned. Repeat with the remaining dumplings. Return cooked dumplings to the baking tray; I like to pat them gently with a paper towel to absorb extra oil, but to not rest them on a towel or they will stick to it.
Air Fry: Spray each side of the dumplings generously with oil and add to your air fryer basket or tray so they are not touching (you will need to work in batches). Air fry at 375F for 8 to 10 minutes, flipping halfway through.
Serve: Serve warm with the dipping sauce. Leftovers can be stored in the refrigerator for up to 3 days. The dumplings will soften in the fridge, but can be reheated on the stove or in the air fryer if you’d like to crisp them up again.