1To make Zeppole:
Cream together the butter and 1/3 c. of sugar until very light. Add the eggs and continue to beat; the mixture will appear broken. Scrape down the sides of the bowl, and then add the vanilla extract and milk.
2In a small bowl, stir together the flour, polenta, baking powder and salt. Add the dry ingredients to the creamed mixture and beat until incorporated. You will have a very soft, sticky dough.Sprinkle the dough liberally with flour and wrap lightly in plastic. Chill until somewhat firm, at least 8 hours.
3When the dough is completely chilled and firm, flour a board liberally and unwrap the dough. Roll to 3/4 inch thickness, using as much flour as needed to prevent the dough from sticking.
4Using a small doughnut cutter, cut out as many as possible; re-rolling the scraps as necessary until you have used all the dough. As you cut the zeppole, place them on a baking sheet sprinkled lightly with flour to prevent them from sticking. Return them to the refrigerator and chill for 30 minutes.
5In a large, heavy bottomed pot, heat the vegetable oil to 340^. Place the remaining 2 cups of sugar in a shallow bowl. Line several baking sheets with 2 layers of paper towels.
6Fry a few at a time in the hot oil, until golden brown on both sides and cooked through. Drain on the towels, and while they are still hot, roll them in the bowl of sugar to coat each one completely. The zeppole may be fried up to 4 hours before serving but they are especially good served hot.
Melt down chocolate chips over a double boiler. Add the espresso and heavy cream and mix to combine. When Zeppoles are ready put chocolate sauce in a little bowl and serve along side as a dipping sauce.