Note: If you plan on saving any of this soup for leftovers, you might consider cooking the wontons in a separate pot of boiling water before adding them to the broth for serving. Because the wontons themselves are coated with cornstarch, they will make the soup cloudy, thick, and starchy, if allowed to sit in the soup for any length of time. You won't have this problem, however, if you choose to serve the soup immediately.
In a large saucepan or soup pot heat the oil over medium high heat until hot. Add 1 tablespoon of the garlic and 1 tablespoon of the ginger and cook, stirring, until fragrant, 1 to 2 minutes. Add the 1/4 cup of sliced scallions and the chicken broth and bring to a boil. Reduce heat to medium low so that the broth just simmers. Allow broth to simmer for at least 20 to 30 minutes while the wontons are being assembled.
In a small mixing bowl combine the remaining teaspoon of minced garlic, remaining tablespoon of chopped ginger, 3 tablespoons of finely chopped scallions, the pork, egg yolk, soy sauce, rice wine vinegar, sesame oil and crushed red pepper. Mix until thoroughly combined.
Working on a flat work surface, lay out a few of the wontons. (Keep remaining wonton wrappers covered with plastic wrap.) Fill a small bowl partially with cool water and set aside. Using a teaspoon measure, place a heaping teaspoonful of the meat filling in the center of each wonton. Using your fingers, lightly wet the edges of the wonton. Bring 2 opposite corners of the wonton together to form a triangle and enclose the filling, pressing edges firmly around the mound of filling to eliminate any air pockets and seal. Moisten opposite corners of the long side. Curl moistened corners toward each other, overlapping one on top of the other, and press the edges together to seal. You should now have a rounded stuffed wonton with a triangle poking up at the top. Assemble the remaining wontons in the same manner. When the wontons are all assembled, set aside.
Add the sliced bok choy, mushrooms, and bamboo shoots to the broth and cook for 2 to 3 minutes. Using your hands or a slotted spoon, gently add the prepared wontons to the simmering broth. Increase the heat slightly so that the broth returns to a gentle simmer. Cook, stirring occasionally (very gently), until the wontons float and the pork filling is cooked through, about 5 minutes. Serve immediately.