Press the block of tofu to expel most of the water and chop all your veggies.
In a medium skillet, saute the mushrooms, carrots, and cabbage in the sesame oil over medium heat for about 5 minutes.
Add in crumbled tofu, green onions, garlic, and ginger. Add salt and pepper to taste. Cook for another few minutes until most of the moisture evaporates.
Set the filling aside to cool. Mix the sauce ingredients together and set aside. Prepare a small dish of water to help moisten the wrapper edges.
Once the filling is cool, take a tbsp and place it in the center of one of the wrappers. Slightly moisten the edges of the wrapper with your finger dipped in water. Press the edges together and make sure they are sealed so no filling will come out. Set aside and repeat with all wrappers until they are filled and sealed.
Heat a small amount of oil in a skillet over medium-high heat. Fry the dumplings in batches for 2-3 minutes per side until nicely browned and crispy. Add a small tablespoon of water to the skillet and cover the pan with a lid to let the dumplings steam for a minute or two, or until all the water is evaporated.
Repeat with remaining dumplings. Serve garnished with extra green onions, sesame seeds, and dipping sauce.
Refrigerate any leftovers in an airtight container for three to four days or freeze for up to three months. Thaw overnight in the fridge before reheating. Alternatively, if making ahead, store filled and assembled dumplings in the fridge or freezer before frying. When ready to prepare, fry fully thawed dumplings before serving.