For the Sfrappole di Carnevale: In a large bowl, combine the flour, butter, yolks, white, sugar, salt, wine and vanilla and mix well to form a dough. Set aside, covered, for 1 hour. Turn the dough out onto a floured work surface and cut it into 4 pieces. Roll each piece out to a 1/2-inch dowel and fashion into small circles, or wheels, measuring 3-inches in diameter. In a tall-sided pot, heat the olive oil to 375 degrees F. Carefully drop the wheels into the oil, working in batches, and cook until golden brown. Remove them carefully with a slotted spoon and drain on paper towels. Sprinkle with confectioners' sugar and serve.
For the Galani di Carnevale: In a large bowl, combine the flour, egg, yolks, butter, salt, vanilla sugar, and wine and mix to form a soft dough. Set aside for 1 hour.
Turn the dough out and roll out to 1/2-inch thickness. Cut the dough into ribbons of varying lengths.
Heat the olive oil to 375 degrees F in a tall-sided pot. Cook the dough strips in the hot oil until golden brown and remove with a slotted spoon to drain. Sprinkle with powdered sugar. Serve at room temperature.
Recipe copyright 2001, Mario Batali. All Rights Reserved.