Add all of the ingredients (except the wrappers, cornstarch, oil, and water) to the bowl of a food processor. Pulse until the mushrooms are finely minced and all of the ingredients are well combined. It will help if you’ve given the mushrooms a bit of a rough chop first, or if you use pre-sliced mushrooms.
Place a won ton wrapper on your work surface, turned so that it appears to be a diamond shape.
Place a teaspoon of filling in the middle of the wrapper.
Dip a fingertip into the bowl of water and trace along the two edges farthest from you. Bring up the end closest to you, fold over the filling, and pinch the edges together to seal. Make sure you’ve gently pressed the wrapper around the filling so there are no air pockets.
Stand up your little triangle pocket so that the filling side sits on your work surface. Fold the top point down, away from you, and pinch. Now, give the edges on either side of that fold 2 little pleats and pinch. Your pot sticker will now look like it has wings. Place it on a large plate that’s been dusted with a bit of cornstarch, to prevent sticking. (Traditionally, pot stickers are made with round dumpling wrappers, so if you have them, you can skip the part about folding the top point down.)
Heat the skillet over medium-high heat. Brush just a few drops of oil onto the hot pan surface, and place 12 of the pot stickers, upright, into the pan. Allow the bottoms to brown. Carefully add 1/2 cup water to the pan and cover it quickly. Cook for about 3-4 minutes, or until all of the water has been absorbed. Remove the pot stickers immediately to another plate to keep warm, and repeat the procedure with the rest of the uncooked ones.
*Feel like you have to have meat? Substitute 4 oz. of ground chicken (or pork, if you must) for half of the mushrooms, just don’t run it through the food processor. Mix the processed ingredients with the ground chicken thoroughly and fill the wrappers as before. Add a full cup of water (instead of 1/2 cup) to the pan, and steam until the water evaporates, about 5-6 minutes.