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1
Trim off and discard mushroom stems. Rinse caps, drain, and cut into 1/4-inch slices.
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2
Cut ham into thin slivers.
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3
Trim off and discard root ends of green onions. Cut off 4 of the longest green spears from onion tops and set aside. Chop white parts of onions and enough of the remaining tops to make 1 cup. Discard remaining tops.
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4
In a 5- to 6-quart nonstick pan over high heat, combine mushrooms, ham, 1/2 cup chopped onions, water chestnuts, cabbage, and ginger. Stir often until mixture is lightly browned, about 8 minutes. Spoon into a bowl.
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5
Pour 1 cup water and enough of the broth into pan to make liquid 1 inch deep. Bring to a boil over high heat.
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6
Immerse reserved green onion tops in liquid just until wilted, 1/2 to 1 minute. Turn heat to low and set a rack in pan above liquid.
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7
Spoon 1/4 of the mushroom mixture onto the center of each egg roll wrapper. Bring corners of wrapper together and tie with a green onion top to enclose filling.
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8
Gently set bundles side by side on rack. Cover pan, turn heat to high, and steam until bundles are slightly translucent and egg roll wrappers are firm (cut a small piece from top to test), about 5 minutes.
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9
With 2 large spoons, gently transfer 1 or 2 bundles to each of 2 soup bowls. Add remaining broth and green onions to pan, bring to a boil, then ladle into bowls. Sprinkle bundles with cilantro leaves.
