In a large bowl, combine the chicken, garlic, green onions, oyster sauce, soy sauce, ginger, and sesame oil.
To assemble the wontons, place wrappers on a work surface. Cover unused wontons with a damp paper towel to prevent them from drying out. Have small bowl of water nearby.
Spoon 3 teaspoons to 1 tablespoon of the chicken mixture into the center of each wrapper. Using your finger, rub the edges of the wrappers with the water. Fold the dough over the filling to create a triangle. Pinching the edges to seal. Dap a little water on the two corners of the triangle. Bring the points together and pinch to seal.
Keep the wontons covered with a damp paper towel to keep them from drying out. Store in the refrigerator until ready to use.
For the soup:
Heat the chicken broth in a large stockpot over medium high heat. Once the broth comes to a boil, add the cabbage, broccoli, and carrots. Reduce heat to a simmer and cook until vegetables are tender, about 5 minutes.
Add the mushrooms and garlic. Simmer for an additional 5 minutes. Stir in the soy sauce, sesame oil, oyster sauce, spinach, thai chili vinegar, and ginger. Carefully stir in the wontons and continue to simmer until the wonton wrappers are opaque and the wontons feel firm, about 2 minutes.