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1
Make dumplings: Place a large pot of water over high heat.
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2
When it boils, add sprouts and onions and cook until sprouts are soft, about five minutes.
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3
Drain in colander and rinse under cold water.
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4
In a large mixing bowl, combine sprouts and onions with kimchi.
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5
Working in batches, transfer a handful to cutting board and mince.
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6
Return vegetables to colander in sink.
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7
Add tofu, tossing to combine.
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8
Press down on vegetables with your hands, draining as much liquid as possible.
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9
Working in batches, place a handful of vegetable-tofu mixture on a large piece of cheesecloth or clean, porous cloth, fold up edges and twist, squeezing out liquid.
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10
Empty back into mixing bowl.
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11
When done, transfer to colander, top with parchment paper and weigh down with a heavy, water-filled pot.
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12
Drain for at least a half-hour.
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13
In a large mixing bowl, combine pork, oil, garlic and salt.
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14
Add drained vegetables and mix well with your fingers.
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15
Place a scant tablespoon of filling in center of a wrapper, brush wrapper rim with egg, and fold, forming a half moon.
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16
Pinch closed with your fingers and squeeze out air.
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17
Wrap end tips around until they touch, dab with egg and pinch together: it will look like a tortelloni.
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18
Transfer to a parchment-lined plate and repeat until you have about 20 dumplings.
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19
Make soup: Place a large pot filled with broth over high heat.
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20
Prepare scallions: discard white parts, chop a few inches of green parts into rounds and slice remainder lengthwise.
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21
When broth boils, add beef and 3 to 4 dumplings a person (freeze unused dumplings), reduce heat to medium and cook 5 to 7 minutes.
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22
Add frozen rice cakes and scallion slices and cook until cakes are soft, another two minutes.
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23
Add eggs and gently stir.
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24
Shut off heat and season with black pepper.
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25
Ladle into bowls and garnish with scallion rounds, sesame seeds and seaweed, if using.