Step 1: Prepare the shrimp dumpling filling. In a medium bowl, combine the finely chopped shrimp, green onions, grated ginger, soy sauce, sesame oil, and white pepper. Mix well.
Step 2: Assemble the dumplings. Lay out a wonton wrapper. Place about 1 teaspoon of filling in the center. Moisten the edges with water and fold into your desired dumpling shape (half-moon or pleats). Repeat with remaining filling and wrappers. If using store-bought, skip this step.
Step 3: Prepare the broth. In a large pot, combine chicken or vegetable broth, minced garlic, grated ginger, chili garlic sauce, soy sauce, rice vinegar, sesame oil, and sugar. Bring to a simmer over medium heat. Taste and adjust seasonings and spice level as desired.
Step 4: Cook the dumplings. Gently add the prepared dumplings (homemade or store-bought) to the simmering broth. Cook for 5-7 minutes, or until the shrimp is cooked through and the wrappers are tender. They should float to the top.
Step 5: Cook the noodles. While the dumplings are cooking, prepare the noodles according to package directions. Most noodles are best cooked separately in their own pot of boiling water, then drained.
Step 6: Serve. Divide the cooked noodles among serving bowls. Ladle the hot spicy shrimp dumpling soup, including dumplings and broth, over the noodles. Garnish generously with fresh sliced green onions and chopped cilantro. Serve immediately.