In a wok or large skillet over medium high heat, add 3 tablespoons of oil and add the ginger. Cook for 30 seconds, until fragrant. Add the onions and stir-fry until translucent.
Add the chopped mushrooms and stir-fry for another 3-5 minutes, until the mushrooms are tender and any liquid released by the mushrooms has cooked off.
Add the cabbage and carrots and stir-fry for another 2 minutes, until the veggies are tender and all the liquid released has been cooked off. Transfer the vegetable mixture to a large mixing bowl and allow it to cool.
To the bowl, add the chopped chives, white pepper, sesame oil, dry sherry, soy sauce, and sugar. Season with salt to taste (though the soy sauce will usually add enough salt to the filling), and stir in the last 1/4 cup of oil
To assemble the dumplings, in one wrap place a hefty teaspoon of filling and pleat the dumplings. Continue assembling until you've run out of filling and/or wraps.
Heat 2 tablespoons of oil in a non-stick pan over medium high heat. Place the dumplings in the pan and allow to fry for 2 minutes. Pour a thin layer of water into the pan, cover, and reduce heat to medium-low. Allow dumplings to steam until the water has evaporated. Remove the cover, increase heat to medium-high and allow to fry for a few more minutes, until the bottoms of the dumplings are golden brown and crisp.