Preheat the oven to 325.
Grease and lightly flour a baking sheet. Blend the flour, sugar, cornmeal, baking powder, and salt. Add the egg and orange juice, and beat the mixture until a dough begins to form.
Add the butter, beating until it is just incorporated, and fold in the pine nuts, basil leaves, and orange zest.
Turn the dough out onto a lightly floured surface, kneading it several times, then let it rest, covered with a kitchen towel, for 5 minutes.
Divide the dough in half and, with floured hands and working quickly on the prepared baking sheet, form each piece of dough into a log 12 inches long by 2 inches wide. Arrange the logs at least 3 inches apart on the middle rack of the oven for 20 to 25 minutes, or until set and pale golden.
Remove them from the oven and let cool on the baking sheet for 10 minutes. On a cutting board, cut the logs crosswise into 1/2-inch-thick slices. Arrange the biscotti, cut side down, on the baking sheet, and bake them 10 to 12 minutes longer.
Remove the baking sheet from the oven, turn the biscotti over, and bake them a final 10 to 12 minutes. Cool completely and store in an airtight container.