Preparation

Make the biscotti

• Combine the flour, brown sugar, ground ginger, baking powder, and salt in a stand mixer fitted with the paddle attachment. Mix briefly on low speed. Add the almonds and crystallized ginger and mix briefly on low speed to combine. Scatter in the butter, and mix on medium speed to incorporate into the mixture. Add the eggs and fresh ginger, and beat on medium speed until a soft, sticky dough forms. Shape the dough into a disk, wrap in plastic wrap or waxed paper, and refrigerate for 1 hour.
• Position a rack in the center of the oven, and heat the oven to 350°F. Line a large rimmed baking sheet with parchment.
• Divide the disk of dough in half. Lightly moisten your hands with water and gently roll one portion into a rough oval. Place it lengthwise on one half of the baking sheet. Use your hands and fingers to stretch and pat the dough into a loaf about 2-1/2 inches wide and 12 to 13 inches long. Repeat with the second piece of dough on the other half of the sheet. Press down on the loaves to flatten them a bit and make the tops even.
• Bake until just set, 20 to 25 minutes; the loaves should be springy to the touch, and there should be cracks on the surface. Transfer the baking sheet to a rack to cool for 5 minutes. Gently remove the loaves from the parchment and let them cool on the rack for 20 minutes.
• Lower the oven temperature to 300°F. Transfer the cooled loaves to a cutting board, and using a serrated bread knife or a santoku knife, cut them on the diagonal into 1/2-inch-thick slices. Arrange the slices, cut side up, on the baking sheet and bake (in batches, if necessary) until lightly browned, about 10 minutes. Turn the slices over and bake until lightly browned, another 10 minutes. Transfer the slices to the rack to cool completely. They will become crisper as they cool.

Make the icing

• In a small bowl, whisk together the confectioners’ sugar, lemon juice, and lemon extract. The icing should be smooth, but still loose enough to fall from the tip of the whisk in a ribbon. If too thick, whisk in a few drops of half-and-half or milk.
• Place the rack of biscotti over a rimmed baking sheet or a sheet of waxed paper or parchment. Dip the tip of the whisk or a fork into the icing and drizzle it back and forth over the biscotti. Let the icing dry completely before serving.

Make Ahead Tips

The biscotti will keep for up to 10 days in an airtight container at room temperature.