Heat the sesame oil in a large skillet over medium heat. Add the mushrooms and cook until browned and water has evaporated off. Stir often, making sure mushrooms don’t stick.
Crumble the tofu in the skillet along with the garlic, ginger and cook until heated through, about 3-5 minutes.
Stir in the soy sauce and scallions, then place entire mixture in a food processor and pulse until coarsely ground.
Take one wonton wrapper and place it on a cutting board, like a diamond. Place ~1 teaspoon of the filling in the middle of the wrapper, then lightly moisten the outside of the wrapper with water. Fold the bottom corner up to meet the top corner, making a triangle. Press down on the filling to squeeze out the air, then press down the edges to seal. Press the left and right sides of the triangle together, moisten the edges and seal.
Repeat with the rest of the filling. Set aside to enjoy now, or freeze on a layer on a baking sheet, then place in a airtight bag or container in the freezer for up to 6 months.
Make the Soup:
Place the mushroom and vegetable broth in a large pot and bring to a boil. Add in the garlic, ginger and cabbage, then stir to dissolve.
Add in the cabbage and simmer over medium heat for 15-20 minutes to let the flavors deepen.
Add the wontons and simmer until the wontons float, about 5 minutes. Remove from heat and stir in the rice vinegar and soy sauce. Stir in scallions and serve.