Cook rice according to package directions, then drain and set aside. Meanwhile, in a small heatproof bowl, soak mushrooms in 1 cup boiling water 15 minutes. Drain, reserving soaking water, and slice mushrooms, discarding stems.
In a wok or large saucepan over medium-high heat, heat oil. Add scallions and ginger and stir-fry 30 seconds. Add crab, mushrooms, salt and pepper, and stir-fry 1 minute.
Add stock, soy sauce, sherry and reserved soaking water and bring to boil. Add peas, reduce heat and simmer, uncovered, about 3 minutes or until tender.
Increase heat to high and bring to boil. Blend in cornstarch mixture, reduce heat and simmer, stirring constantly, about 1 minute or until slightly thick. Remove from heat and slowly add eggs in a thin stream. Stir in sesame oil. Divide reserved rice among 4 bowls, ladle in crab and black mushroom soup and sprinkle with scallion tops, if desired.