Chop ginger, green onion, garlic, water chestnuts (if using), and carrots (if using). Place into a small bowl with ground meat or meat substitute.
In the same bowl, add soy sauce, black pepper, and whisked egg (if using). Mix gently to combine.
To assemble the wontons, add a small amount of filling (about 1 tbsp or less) to the center of the wonton wrapper. Then, wet all four edges of the wonton wrapper and fold in half diagonally to create a triangle shape.
Take the left and right sides of the triangle and fold them inwards towards the center; it should look like the wonton is giving itself a hug. Add more water to the edges if needed, for a good seal.
Make sure all edges of your wontons are completely sealed and there are no air bubbles inside, otherwise the filling will explode and the wonton will fall apart during the cooking process.
Set aside while you make your soup broth.