In a large bowl, beat the eggs and sugar together at high speed with an electric mixer until foamy, about 5 minutes. Add the orange zest and juice, oil, almond extract and vanilla extract, beating until blended. Sift the flour and baking powder together and add to the egg mixture, beating well. Fold in the almonds by hand. Remove the dough to plastic wrap, wrap and freeze until firm, about 30 minutes.
Meanwhile, preheat the oven to 325 degrees F. Spray a baking sheet with nonstick cooking spray. Divide the dough in half. Spray your hands lightly with nonstick cooking spray and shape each portion into a 5-by-8-inch log on the baking sheet. Bake until firm, about 25 minutes. Cool the logs on the baking sheet for 5 minutes, then transfer to wire racks to cool completely, about 15 minutes.
Using a serrated knife, cut each log diagonally into 1/2-inch slices. Return the biscotti to the baking sheets and bake for 15 minutes. Turn the cookies over and bake for 15 more minutes. Cool on wire racks.