Preheat the oven to 325 degrees F.
Line a large baking sheet with parchment paper. Stir the flour, cornmeal, baking powder, and salt in a large bowl. Using an electric mixer, beat the eggs and sugar in another large bowl until pale yellow and fluffy, about 3 minutes. Add the orange and lemon zests to the dry ingredients. Add the flour mixture to the eggs and sugar and beat just until blended (the dough will be soft and sticky). Let stand for 5 minutes.
Using a rubber spatula, transfer the dough to the prepared baking sheet, forming two mounds spaced evenly apart. Moisten your hands with water and shape the dough into two 11 by 4-inch logs. Bake until lightly brown, about 35 minutes. Cool the logs for 5 minutes. Using a serrated knife, cut the logs crosswise into 1/2-inch-thick diagonal slices. Arrange the biscotti cut side down on the same baking sheet. Bake until the biscotti are pale and golden, about 25 minutes. Cool the biscotti on the baking sheet for 5 minutes. Using a metal spatula, transfer the biscotti to a rack and cool completely.
Melt the chocolate chips in the microwave, stirring every 20 seconds, about 1 1/2 minutes total. Dip 1 cut side of each biscotti into the melted chocolate. Gently shake off the excess chocolate. Place the biscotti, chocolate side up, on the baking sheet. Refrigerate until the chocolate is firm, about 35 minutes. Dip a pastry brush in the cocoa, then lightly brush the cocoa over the chocolate on each biscotti.
The biscotti can be made ahead. Store them in an airtight container up to 4 days, or wrap them in foil and freeze in resealable plastic bags up to 3 weeks.