POUR the water into a small bowl, and then add the yeast and stir until completely dissolved. Set aside.
Scald the milk and let cool to lukewarm.
Add the milk to the dissolved yeast.
BLEND together the eggs, margarine, sugar, salt, and nutmeg until well blended, and then add to the milk and yeast mixture.
Gradually add the flour until the dough is elastic and easy to handle.
Put in a warm place.
Cover with waxed paper and let rise until double in size, about 2 hours.
Punch down and divide the dough into two large pieces.
Roll out each piece to a ¾-inch thickness and cut into 7-inch-long oblong pieces.
LET rise again.
Heat vegetable shortening in a deep pan to a depth of 2 to 3 inches until very hot.
Fry the rolls in batches until golden, 2 minutes on each side.
TO MAKE THE FROSTING: Cream the butter with the vanilla and 1 cup of the powdered sugar in a medium bowl.
Gradually add the milk and the remaining powdered sugar and stir until smooth.
Frosting may be added if desired, once the rolls have cooled.