For the dipping sauce: In a medium bowl, add the soy sauce, oil, sesame seeds, vinegar and scallions. Stir to combine. Cover and refrigerate until needed.
For the dumplings: Bring a pot of water to a boil and set up an ice bath. Blanch the bean sprouts in the boiling water for 30 seconds, then drain and pour into the ice water. When cool, drain and set aside.
Using a potato masher, mash the tofu until smooth. Set aside.
In a large bowl, add the beans sprouts, mashed tofu, beef, pork, sesame oil, ginger, garlic, carrots, 3 of the eggs, the onions, cabbage and scallions. Using your hands, mix the ingredients until thoroughly combined.
Place 1 wonton skin on a flat surface. Using your finger, coat the outer edges of the wonton with the remaining beaten egg. Place 1 tablespoon of the filling in the center of each wonton and fold the skin in half over the filling to form a triangle. Press the edges together to seal, making sure no filling leaks through. Repeat for the remaining wonton skins.
Heat a 10-inch skillet over medium-high heat. Add enough peanut oil to generously coat the bottom of the skillet. Place some dumplings into the skillet 1/4-inch apart, and cook cook until golden brown and the edges are crisped, 3 to 4 minutes per side. Add 1/4 cup of water to the skillet and cover with a lid and steam for 4 to 5 minutes. Repeat for the remaining dumplings. Transfer the dumplings onto a platter and serve with the dipping sauce.
A viewer or guest of the show, who may not be a professional cook, provided this recipe. It has not been tested for home use.