Place the mung beans in a saucepan set over moderate heat with
1/2 cup of the water and bring to a boil, stirring occassionally.
Reduce the heat to low, cover and simmer until all the liquid
has been absorbed, about 10 minutes. Remove any bean skins from
the pot.
Increase the hear to medium-high. Add the coconut milk,
3 tablespoons of sugar and the salt and cook, stirring and
scraping constantly, until the beans become thick and begin
to pull away from the sides of the pan, 7 to 8 minutes. Remove
from the heat and allow to cool slightly.
Transfer the beans to a blender or food processor and process
until smooth and thick ( if the mixture is too thin to be
molded into rolls, return to pan and cook until sufficiently
thickened.)
Meanwhile, press the yolks through a fine sieve set over
a bowl by rubbing them back and forth gently with a spoon
-- this can take several minutes. Set aside.
To prepare the syrup, put the remaining 1 1/2 cups of water
in a medium saucepan, bring to a boil and add the remaining
1 cup of sugar, stirring to dissolve. Return to a boil, reduce
the heat to low and allow to simmer without stirring until
the mixture thinckens slightly.
Meanwhile, once the mung bean paste is cool enough to handle,
roll out small amounts into little sausage shapes, about 1
1/2 inches long and 3/4 inches in diameter. In batches , dip
the mung bean rolls into the prepared egg yolks to coat, then
drop them into simmering syrup, without crowding , and cook
for 2 minutes, turning once after about 1 minute. The egg
coating will be opaque and shiny. Remove with a slotted spoon
and serve warm or at room temperature.