In a food processor, pulse together the flour and cornmeal to blend. Cut the butter into 9 pieces and add to the food processor. Pulse until the butter is blended into the dry ingredients. Transfer the mixture to a bowl and mix in the currants or blueberries.
Beat the eggs, grated lemon peel (if using), vanilla, and two tablespoons water into the dry ingredients. Divide the dough into 3 parts.
Place the pieces of dough on a non-stick baking sheet. Shape each piece into a long rounded-top, flattened log, 2-1/2-inches x 8-inches x 1-inch.
Bake at 350 degrees F for about 20 minutes, until the dough is a light gold. Let cool 5 minutes. Cut each log diagonally into 3/4-inch slices. Place the slices, cut side down, on the baking sheet.
Bake the biscotti 5 minutes. Turn them over and bake 5 minutes longer, until they are firm. Transfer the cookies to a rack and cool completely.