Place the dried shiitake mushrooms in a small heatproof bowl and cover with boiling water. Allow to soak for 30 minutes. Drain, rinse, and cut into thin slices. Set aside.
In a large saucepan, heat the chicken stock. Add the ginger, garlic, chile paste, vinegar, soy sauce, reconstituted shiitake mushrooms, and bamboo shoots. Simmer for 10 minutes. Add the lime juice and sugar and season to taste with salt.
Make a cornstarch slurry by mixing together the cornstarch and water. Add the slurry to the soup and simmer for a few minutes until the soup thickens. Bring the soup to a boil and slowly pour in the beaten egg, stirring gently a few times with a spoon or with chopsticks. Don't whisk or stir too vigorously--you want nice long shreds of egg. The egg will cook almost instantly. Remove the soup from the heat.
On the plate: Ladle the soup into 4 bowls. Top each bowl with an ounce of crabmeat and garnish with the green onions.
