Combine the butter, salt, 2 tablespoons sugar, apple juice and 1/2 cup water in a medium saucepan. Bring to a boil over medium heat. Off the heat, stir in the flour; then return the pan to the heat and cook, stirring continuously, until the mixture forms a ball, about 2 minutes. Transfer the cooked flour mixture to a medium bowl. Using an electric hand mixer on low speed, add the eggs one at a time, incorporating each egg completely before adding the next. Beat until smooth. If not frying immediately, cover the bowl with plastic wrap and reserve in the refrigerator.
Pour enough oil into a large frying pan to reach a depth of 2 inches. Heat over medium heat until the oil registers 350 degrees F on a deep-fry thermometer. Using a small ice cream scoop or two small spoons, scoop out 1 tablespoon of dough and push two of the frozen candies into its center. Smooth the dough over the candies to fully encase them. Carefully drop the filled dough into the hot oil. Fry in batches, turning the zeppole once or twice, until they are golden and puffed up, about 5 minutes. Drain on paper towels.
Combine the remaining 2 tablespoons sugar and the cinnamon in a small bowl. Toss the fried zeppole in the cinnamon-sugar. Arrange on a platter and serve immediately.
Recipe courtesy of Giada De Laurentiis