Clean the shiitake mushrooms and remove the stems. Finely dice the caps and place them in a medium bowl. Stir in the garlic, ginger, soy sauce, sesame oil, liquid smoke, if using, and scallion.
Fill a small bowl with water. Arrange a wonton wrapper on work surface. Place about 1 teaspoon of filling in center. Dip fingers in water and moisten the edges of the wonton wrapper. Fold in half, over filling, diagonally, to create a triangle. Press the edges together to seal. Draw the side corners of the wrapper inward, join and press them together to seal, creating a loop. Repeat until all of the filling and wrappers are used.
Coat the bottom of a large pot with the vegetable oil and sesame oil, and place it medium heat. Add the garlic and ginger. Sauté for 1 minute, until very fragrant. Add broth, raise the heat, and bring it to a boil. Add the wontons and lower the heat to a simmer. Allow the soup to simmer until all of the wontons float, about 5 minutes. Stir in the napa cabbage and vinegar. Remove from heat and season with soy sauce or salt to taste.
Ladle into bowls and top with scallions. Serve.
Make sure you read the ingredients on your wonton wrappers, as many brands contain egg.