Preheat the oven to 350°. Line 2 baking sheets with parchment paper for the biscotti.
Spread the pecans on a rimmed baking sheet and bake for 10 minutes, or until lightly toasted and fragrant; let cool. In a medium saucepan, cook the butter over moderate heat until brown and fragrant, about 8 minutes. Pour the butter onto a rimmed baking sheet to harden.
In a medium bowl, whisk the 2 cups of flour with the baking powder and salt. In another medium bowl, using an electric mixer, beat the browned butter with the sugar until combined. At low speed, beat in the eggs, 1 at a time, until incorporated. Beat in the vanilla. Gradually beat in the dry ingredients, then stir in the pecans.
Gather the dough into a ball. Divide the dough in half. Shape each piece of dough into a 14-inch-long log on 1 of the baking sheets. Gently flatten the logs until they are 1 1/2 inches thick.
Bake the logs for 25 minutes, or until golden and lightly cracked on top. Remove the logs from the oven. Using a serrated knife, cut the warm logs diagonally into 3/8-inch-thick slices. Arrange the slices on their sides on the baking sheets and bake for about 20 minutes, or until golden. Transfer the biscotti to racks to cool.
The biscotti can be stored in an airtight container for 2 weeks.