Preheat the oven to 350 degrees F. Line a large rimmed baking sheet with parchment paper.
Combine the sugar and butter in the bowl of a standing mixer fitted with a paddle. Cream the mixture until pale and fluffy. Add the eggs, one at a time, making sure to mix well before each addition. Add the orange zest and basil and blend on low speed, about 30 seconds.
Combine the flour, baking powder and salt in a separate bowl. Add the flour mixture to the standing mixer and beat until combined. Fold in the almonds.
Transfer the dough to a lightly floured surface. Divide the dough in half. Using floured hands, shape the dough into logs. Brush off the excess flour. Place the logs on the baking sheet, spaced 5 inches apart.
Flatten each log into a 2-inch-wide strip. Bake the logs, rotating the baking sheet halfway through, until browned and set, about 30 minutes. Transfer the logs to a cooling rack and cool, about 15 minutes.
Reduce the oven to 300 degrees F.
Transfer the logs to a work surface. Cut each log diagonally into 1/3-inch-thick slices using a serrated knife. Arrange the slices, cut-side down, on the baking sheet. Bake the slices, rotating the baking sheet halfway through, until crisp, about 20 minutes. Transfer the slices to the cooling racks and let cool.
The biscotti can be made 3 days ahead and stored in an airtight container at room temperature.