In a pot of boiling water, cook the noodles according to package directions. Drain and rinse.
Meanwhile, in a saucepan, bring 2 cups water, the chicken broth and ginger to a boil. Stir in the soy sauce and lower the heat to low.
Divide the chicken, snow peas and coleslaw among 4 large soup bowls. Add the noodles to the saucepan and heat through. Using tongs, divide the noodles among the soup bowls. Ladle the liquid into the bowls and top with the scallions and cilantro. Serve with the chili paste.