1. Preheat oven to 375°F. Line a large baking sheet with parchment paper; set aside. Place cranberries in a small bowl, and add boiling water. Let stand until plump, about 15 minutes. Drain, pat dry, and set aside. Sift together flour, baking powder, and salt into a medium bowl; set aside.
2. In the bowl of an electric mixer fitted with the paddle attachment, beat the butter and sugar on medium speed until light and fluffy, about 2 minutes. Add 3 eggs, one at a time, beating to incorporate after each addition and scraping down the sides of the bowl as needed. Beat in vanilla and almond extracts. Add teh flour mixture, and mix on low speed until combined. Mix in the drained cranberries and the white chocolate chips.
3. Turn out dough onto a lightly floured surface; divide in half. Shape each piece into a 16-by-2-inch log, and transfer to prepared baking sheet, about 3 inches apart. With the palm of your hand, flatten logs slightly. Brush beaten egg over the surface of the dough logs, and sprinkle generously with sugar.
4. Bake, rotating sheet halfway through, until logs are slightly firm to the touch, about 25 minutes. Transfer logs on parchment paper to a wire rack to cool slightly, about 20 minutes. Reduce oven temperature to 300°F.
5. Place logs on a cutting board. Using a serrated knife, cut the logs crosswise on the diagonal into ½-inch-thick slices. Place a wire rack on a large rimmed baking sheet. Arrange slices, cut sides down, on the rack. Bake until firm to the touch, about 30 minutes. Remove pan from oven; let biscotti cool completely on the rack. Biscotti can be kept in an airtight container at room temperature for up to 1 week.