Method:
Several hours or day before serving prepare vegetable broth: In 4 quart sauce pot, combine water, carrot, onion, dried mushrooms, white part of green onions (save green part), garlic, ginger root, salt, soy sauce, and honey. Heat to boiling then reduce heat to low and simmer, partially covered, for 45 minutes. Cool, then refrigerate overnight or for at least 2 hours.
Strain broth, discarding all vegetables except mushrooms. Return broth and mushrooms to saucepot; add red pepper, cover and cook over medium-low heat for 10 minutes.
Meanwhile, cook Chinese noodles following package directions. Drains noodles and toss with sesame oil. Coarsely chop green tops of green onions. Add noodles and onions to broth; simmer 3 minutes. To serve soup, divide between 4 serving bowls.