Cover mushrooms with boiling hot water in a small bowl and let stand 30 minutes, then squeeze excess water from mushrooms and reserve 1 cup mushroom-soaking liquid.
Discard mushroom stems and cut caps into very thin slices.
Meanwhile, mix together pork,scallions,water chestnuts,rice wine,sesame oil, sugar, 1 tablespoon ginger,1 tablespoon soy sauce, and 1/2 teaspoon salt in a large bowl with your hands.
Gather together pork mixture and throw against bottom or side of bowl 5 or 6 times to firm texture, then chill, covered, until ready to use.
Remove and reserve 4 large cabbage leaves.
Halve cabbage head lengthwise, then cut out and discard core.
Cut cabbage leaves crosswise into 2 inch pieces.
Heat wok over high heat until a drop of water evaporates instantly; swirl 2 tablespoons oil to coat bottom and sides of wok, then stir-fry mushrooms, half of cabbage, and remaining tablespoon of ginger until cabbage begins to wilt,about 1 to 2 minutes.
Add remaining cabbage and 3/4 teaspoon salt and stir-fry until all of cabbage has begun to wilt, about 3 minutes.
Add reserved soaking liquid (1 cup) and continue stir-frying until cabbage is wilted, about 3 minutes.
Transfer mixture to a 4 to 5 quart heavy pot, arranging evenly on bottom; wipe wok clean with paper towels.
Stir together cornstarch, pepper, and remaining soy sauce in a small bowl until smooth.
Divide pork mixture into quarters, then coat your hands with some of cornstarch/soy sauce mixture.
Form 4 large meatballs, transfering each as formed to a large plate and then recoating your hands.
Heat wok over high heat until a drop of water evaporates instantly, then pour in remaining oil, enough to measure a scant 1/4 inch in wok.
Reduce heat to moderately high and gently arrange meatballs in wok.
Fry meatballs, turning gently until deep golden on all sides, about 5 minutes total; if meatballs stick, add a little more oil.
Transfer with a slotted spoon to paper towels to drain, then arrange on top of cabbage in pot.
Add broth, then cover meatballs completely with reserved 4 cabbage leaves.
Bring liquid just to boil, then reduce heat and gently simmer, covered, 1 hour; check frequently to make sure liquid is not boiling vigorously.
Season broth with salt, then move large cabbage leaves around the edge of pot to resemble a lion's mane.
Serve in individual shallow bowls over rice, if desired.