In a bowl, combine the shrimp, mushrooms, green onions, sesame oil, ginger, garlic, salt, pepper and cooking wine. Stir until thoroughly combined, then set aside.
Add water to a small bowl, and place it nearby.
Peel off one wonton skin from the pack, then cover the rest with a slightly damp towel so they don't dry out.
Use a spoon to add a small amount of filling to the middle of the wonton skin. Be careful not to add too much, or your wontons will burst while cooking.
Use your finger to moisten the edges of the wonton skin. Then fold it in half to create a triangle.
Press down the edges to seal the wonton, making sure to remove as much air as possible. You can leave the wonton as a triangle, or continue folding into desired shape.
Place wrapped wonton on a tray lined with parchment paper, and then continue to make the rest of your wontons.
Fill a deep heavy pot with cooking oil until it fills about ¼ of the pot. Heat the oil to 375°F.
While the oil is heating up, line a plate or tray with paper towels and set aside.
Once the oil is hot, carefully add a few wontons to the pot. Fry the wontons, turning them as needed, until they are golden brown all over. This should take 2-3 minutes.
Use a strainer or slotted spoon to remove the cooked wontons from the hot oil. Place on prepared plate or tray to drain.
Cut one of the wontons and check to make sure the filling is cooked. If it is still raw, reduce the temperature of your oil a little so the wontons can spend more time in the hot oil.
Eat cooked wontons immediately for best texture.
To Make the Dipping Sauce:
Combine all ingredients in a bowl and serve.
Notes
Tip: If your wontons have become wet because you used too much water to seal them, allow them to dry out before you fry them. You may need to flip them over to dry both sides.