In a medium saucepan combine the butter, salt, sugar, and water over medium heat. Bring to a boil. Take pan off the heat and stir in the flour. Return the pan to medium heat and stir continuously until mixture forms a ball, about 3 to 5 minutes. Transfer the flour mixture to a medium bowl. Using an electric hand mixer on low speed, add eggs, one at a time, incorporating each egg completely before adding the next. Beat until smooth. Add the grated apple and stir to combine. If not frying immediately, cover with plastic wrap and reserve in the refrigerator.
Combine the whipping cream, 2 tablespoons confectioners' sugar, and cinnamon in a medium bowl. Whip until medium soft peaks form. Transfer the whipping cream to a serving dish.
Meanwhile, pour enough oil into a large frying pan to reach a depth of 2 inches. Heat the oil over medium heat until a deep-fry thermometer registers 325 degrees F.
Using a small ice-cream scooper or 2 small spoons, carefully drop about a rounded tablespoon of the dough into the hot olive oil. Turn the zeppole once or twice, and cook until golden and puffed up, about 4 minutes. Fry the zeppole in batches so as not to overcrowd the pan. Drain on paper towels.