Transfer to a saucepan, add the salt and water and bring to a boil.
Simmer over moderate heat for 10 minutes.
Strain the ginger broth through a fine sieve, discarding the ginger.
Return the broth to the saucepan and bring to a boil.
Add the shrimp and cook over high heat just until opaque, about 1 minute.
Remove the shrimp to a plate with a slotted spoon and let cool.
Let the cooking liquid cool too, then add the shrimp and refrigerate until chilled, at least 30 minutes.
Drain the shrimp and pat dry.
In a large pot of boiling water, cook the cabbage until tender, about 2 minutes.
Drain and let cool under running water, then dry the cabbage leaves thoroughly with paper towels.
Cut the cabbage into 6-by-1-inch strips.
Set a shrimp at one end of a cabbage strip, top with a scant 1/8 teaspoon of the black bean-chili sauce and a few of the sprouts and roll up the shrimp in the cabbage strip.