Heat wok over medium-high heat, add 2 tablespoons oil and cook meat until brown, mashing with a fork to break into small pieces. Drain off fat and set meat aside. Rinse and dry pan.
Heat 1 tablespoon oil over high heat for one minute, then add the onions and sauté them for 2 to 3 minutes, or until soft.
Add cabbage or kimchi and continue to cook, stirring frequently, for another 2 to 3 minutes or until cabbage is crisp-tender. Add bean sprouts, green onion and tofu, mix well and cook for 1 to 2 minutes more.
Remove pan from heat and pour cooked mixture into a colander to drain excess liquid.
In a large bowl, combine meat, vegetables, hoisin, salt and pepper and mix well.
Place 1 wonton skin on a flat surface. Cover remaining skins with a slightly damp kitchen towel (not terry cloth) so they won't dry out. Brush the edges of skin with beaten egg. Place about 1 teaspoon of filling mixture just above the center of skin. Fold skin in half over filling to form a triangle and press edges together to seal. Repeat with remaining skins.
Heat a skillet with just enough vegetable oil to coat the bottom surface. Feel free to use two skillets to speed up the cooking process. When the oil is very hot, gently place a layer of mandu in the skillet, being careful not to overlap them. Once they are browned on the bottom, flip them over, and quickly add 2 tablespoons water to the pan, cover it and steam the mandu until they are cooked through. This should take about 2 minutes.
Once they are ready, mandu may be arranged in a serving dish or kept warm in a low oven while the remainder are cooked.
Prepare dipping sauce by combining all ingredients in a bowl. Stir to dissolve sugar.
Serve the mandu with dipping sauce.