Place noodles (discard seasoning packages) in a large bowl; cover with boiling water. Soak 3 minutes; drain under running water. Divide among 4 soup bowls.
Heat oil in a medium saucepan over medium heat. Stir-fry ginger and garlic about 30 seconds. Add broth, soy sauce, chili-garlic sauce, chicken, and pepper to taste; bring to a boil. Reduce heat to low; simmer about 5 minutes, or until chicken is done. Remove from heat; stir in scallions. Ladle soup over noodles. Top with 1/2 cup spinach and chili-garlic sauce to taste.