1. Soak the kombu in ½ cup of water for 30 minutes. Stir in 1/3 cup of flour, mix to a paste, and set aside.
2. Puree the shrimp, a few at a time, in an electric blender or put them twice through the finest blade of a meat grinder.
3. Then, with an electric beater or large spoon, beat into the puree the salt, mirin, 1 egg white and 6 tablespoons of the flour-and-kombu liquid. Continue to beat until smooth.
4. With a small, sharp knife, trim the turnips into 1h-inch balls. Divide the shrimp mixture into 6 parts and, moistening your hands with cold water, shape into 6 balls.
5. Make an indentation in the top of each ball and force the turnip into it. Pat into shape again, enclosing the turnip.
6. Spread the cut noodles out on a sheet of wax paper. Then roll the shrimp balls about in them until they adhere and protrude like thorns.
7. Pour into a deep-fat fryer or deep skillet enough oil to come 3 inches up the sides. Set over high heat until the oil registers 375° on a deep fat thermometer. Deep-fry the shrimp balls 3 or 4 at a time for 2 to 3 minutes, or until they are golden brown.
8. Remove and drain on paper towels. With a chopstick or the point of a knife, make a hole in the top of each ball and spread it open gently. One by one, remove the turnips and insert a sweet chestnut in its place. Serve at room temperature.
