To make zeppole, deep fry tablespoon-sized balls of batter and toss them in a mixture of cinnamon, sugar and vanilla seeds. Create the batter by combining butter, salt, sugar, water, flour and eggs into a smooth mixture.
Start by cutting open one vanilla bean lengthwise and scraping its seeds out into a bowl. Then, mix 1/2 cup and 3 tablespoons of sugar with 2 tablespoons of ground cinnamon in with the seeds and stir. Set this mixture aside.
Next, combine 1 stick of butter, 1/4 teaspoon of salt, 3 tablespoons of sugar and 1 cup of water into a medium saucepan. Bring to a boil over medium heat. Next, remove the pan from the heat, and add one cup of all-purpose flour to the mix. Return the pan to the heat, and stir for 5 minutes or until the mixture forms into a ball. When a ball forms, place the mixture into a separate bowl, and add four eggs into the mix using an electric hand mixer on a low setting. Be sure to incorporate each egg smoothly into the mix before adding the next egg.
Next, fill a large frying pan with 2 inches of oil and heat it up to 375 degrees. Drop a tablespoon of the dough mixture into the oil using an ice-cream scooper or two spoons. Fry the dough in batches for five minutes or until each batch becomes puffy and golden-colored, turning over each zeppole once or twice during the frying. After frying, drain the zeppole on paper towels. Toss the balls in the cinnamon-and-sugar mixture, and serve immediately.