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1
In a small bowl, cover the dried mushroom with hot water and let stand until softened, about 5 minutes.
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2
Drain and coarsely chop the mushroom.
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3
Peel and devein the shrimp, reserving 20 with their tails.
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4
Coarsely chop the remaining shrimp.
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5
In a food processor, finely chop the carrot.
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6
Add the onion and mushroom and finely chop.
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7
Add the chopped shrimp, fish sauce, oil, salt and pepper; process just until blended.
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8
If using spring roll wrappers, cut them in half diagonally to form 2 triangles.
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9
Lay 2 of the triangles on a work surface with the long side facing down; keep the remaining wrappers covered with a damp towel.
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10
Place a whole shrimp in the center of each wrapper with the tail sticking up beyond the tip of the triangle.
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11
Spread 1 scant tablespoon of the chopped filling over each shrimp and brush the edges of the wrappers with a little beaten egg.
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12
Fold the longest side of each wrapper up and over the shrimp, wrapping the ends tightly around it.
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13
If using wonton wrappers, lay one on a work surface and brush the edges with egg.
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14
Set a shrimp in the center, with the tail sticking out of the wrapper.
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15
Spread with 1 tablespoon of the filling and cover with another wrapper.
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16
Repeat with the remaining wrappers, shrimp and filling.
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17
In a heavy saucepan, heat the vegetable oil to 350 over moderately high heat.
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18
Fry 3 or 4 dumplings at a time, turning once, until golden brown and crisp, 4 to 5 minutes.
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19
If necessary, lower the heat so that the oil won't smoke.
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20
Drain the dumplings briefly on paper towels, then transfer to a platter and keep warm.
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21
Serve with a bowl of Nuoc Cham.