Pre-soak the dried shiitake mushrooms with water for 20 minutes. Squeeze out any water from the mushrooms (if using fresh mushrooms, skip this step) and remove and discard the stems. Dice the mushrooms into small cubes.
Combine the diced mushrooms, ground chicken, and chopped scallions in a bowl; season them with Chinese Shaoxing cooking wine, soy sauce, oyster sauce, salt, sugar, sesame oil and ground white pepper. Stir well with a spatula or a pair of chopsticks. Marinate the filling in the refrigerator for 30 minutes.
Prepare a small bowl of water nearby. Place one wonton wrapper on your palm and add one teaspoon of filling in the center of the wonton wrapper. Wet your finger; dab the edges along one side of the wonton wrapper with water.
Fold the wonton wrapper in half to become a rectangle. Pinch the sides to seal the filling inside.
Dab one bottom corner of the wonton wrapper with water. Gather two corners of the wrapper with thumb and index fingers on both hands and press down. Make sure the wontons are sealed tight. Repeat until the filling is used up.
Prepare the soup by adding the chicken bouillon powder, salt, white pepper and sesame oil to a bowl. Pour the boiling water into the bowl, and stir well.
Bring the water to a boil in a pot. Drop the wontons into the water and stir gently to avoid them sticking together. Cook the wontons without a lid and continue to boil until they float to the top and are cooked through.
Turn off the heat. Drain the wontons with a strainer and transfer them into the soup. Serve immediately.