Cut open the vanilla bean lengthwise. Using the back of a knife, scrape along the inside of the vanilla bean to collect the seeds. Scrape vanilla bean seeds into a small bowl. Add the 1/2 cup sugar and cinnamon and stir to combine. Set aside.
In a medium saucepan combine the butter, salt, 3 tablespoons of sugar, and water over medium heat. Bring to a boil. Take pan off the heat and stir in the flour. Return pan to the 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, 1 at a time, incorporating each egg completely before adding the next. Beat until smooth. If not frying immediately, cover with plastic wrap and reserve in the refrigerator.
Using a small ice-cream scooper or 2 small spoons, carefully drop about a tablespoon of the dough into the hot olive oil, frying in batches. Turn the zeppole once or twice, cooking until golden and puffed up, about 5 minutes. Drain on paper towels. Toss with cinnamon-sugar. Arrange on a platter and serve immediately.
Recipe courtesy Giada De Laurentiis