In a 5- to 6-quart pan, mix cornstarch with a little of the broth. Then add remaining broth, vermouth, soy sauce, ginger, lemon peel, lemon juice, and thyme.
Stirring often, bring the broth mixture to a boil over high heat. Add crab, reduce heat, and simmer, continuing to stir often, until crab is hot, about 5 minutes. Sprinkle with parsley.
Ladle crab and broth equally into wide bowls.