Stir the sugar, salt and yeast into the warm water and allow to proof for about 15 minutes. The yeast will be activated and have the appearance of a head of beer. If it does not, it should be discarded and replaced with fresh yeast. (Improper storage temperature will sometimes destroy yeast even if the date on the package indicates it has not yet expired.)
Add the flour and nutmeg to a food processor fitted with a dough blade (or the bowl of a mixer fitted with a dough hook). Turn on the food processor and through the feed tube, gradually add the yeast mixture. (Or turn on the mixer and gradually add the yeast mixture to the bowl of flour.) Then add the olive oil and eggs. Mix until the dough comes together.
Transfer the dough to a large bowl and cover with a clean damp towel. Let rise in a warm place for about 1 hour. Punch down the dough and let it rise a second time in the same way. This will make the texture of the dough finer. Please note that the dough will not rise as much the second time.
Heat oil in deep-fryer to 375 degrees F. or as directed on the manufacturer's instructions for similar foods. Transfer the dough to a lightly oiled marble slab and knead for a few minutes. Divide the dough into eighths. Divide each eighth into thirds and roll into a cylinder about 1/2-inch in diameter and 8 inches long. Connect the 2 ends of the cylinder and press firmly to make a circle. Grab the circle on each side and twist twice. Add zeppole to basket immersed in oil in deep-fryer and fry until golden. Remove and drain on paper towels. Sift confectioners' sugar over them while they are still warm.