Step 1In a large bowl, whisk together the flour, sugar, baking powder and salt. Make a well in the center. In a medium bowl, lightly beat the eggs with a fork. Gradually stir in the olive oil until well blended, followed by the limoncello, vanilla and zest. Pour the olive oil mixture into the center of the flour mixture. Using a whisk or a wooden spoon, and stirring from the center, gradually combine the ingredients to fully incorporate and form a sticky dough.
Step 2Add the nuts to the bowl. Using your hands, gently incorporate them into the dough while forming a ball. If the mixture becomes sticky, moisten your hands with water. Cover the bowl with a plate and set aside for 25 to 30 minutes.
Step 3Meanwhile, place a rack in the center of the oven and heat to 350 degrees. Line a large rimless baking sheet with parchment paper. Lightly grease the work surface with olive oil.
Step 4Cut the dough inside the bowl into 4 equal pieces. Gently form each piece into a log, about 9 inches long, pressing in any protruding nuts and moistening your hands with water if needed to keep the dough from sticking. Place the logs crosswise on the baking sheet, leaving at least 2 inches in between. Gently pat down the top of each log until it is about 13/4 inches wide. Sprinkle each log with a scant teaspoon sugar.
Step 5Bake until the logs firm up, small cracks appear on top and their edges turn golden brown, about 25 minutes. Remove the baking sheet from the oven and carefully slide the parchment paper with the logs onto a wire rack. Set aside to cool for 25 to 30 minutes.
Step 6Reduce the oven temperature to 300 degrees. Place a fresh sheet of parchment on the baking sheet. Transfer the logs to a cutting board (loosen them with a metal spatula if needed). Using a large serrated knife, cut each log diagonally into 1/2-inch-thick slices. Place the slices, cut side down, onto the baking sheet without touching.
Step 7Bake until the biscotti are fragrant, feel dry to the touch and start to brown around the edges, 30 to 35 minutes. Carefully slide the parchment paper with the biscotti to a wire rack to cool completely before storing.