Heat 1 tablespoon vegetable oil in a medium skillet over medium high heat. Add mushrooms and shallots, and cook, stirring occasionally, until tender, about 3-4 minutes. Stir in cabbage and carrots until tender, about 3-5 minutes. Let cool completely.

In a large bowl, combine mushroom mixture, water chestnuts, cilantro, egg, garlic, ginger, soy sauce, rice wine vinegar and sesame oil; season with salt and pepper, to taste.

To assemble the potstickers, place wrappers on a work surface. Spoon 1 tablespoon of the mushroom mixture into the center of each wrapper. Using your finger, rub the edges of the wrappers with water. Fold the dough over the filling to create a half-moon shape, pinching the edges to seal.*

Heat remaining 2 tablespoons vegetable oil in a large skillet over medium heat. Working in batches, add potstickers in a single layer and cook until beginning to crisp on the bottom, about 2-3 minutes. Working quickly, add 1/4 cup water; cover and cook until liquid has evaporated and bottoms of dumplings are crisp and golden, about 3-5 minutes.

Serve immediately.