Preheat the oven to 350 degrees. Line a baking sheet with parchment paper, set aside.
Melt butter in a large skillet over medium heat; add nuts. Cook, stirring constantly, until nuts are browned. Remove from heat and cool completely. Watch the pecans carefully as they can burn fast. Allow them to cool and then chop the pecans; set aside
In a medium bowl, whisk together flour, baking powder, salt, and pumpkin pie spice; set aside.
In the bowl of a stand mixer, combine the eggs, brown sugar, pumpkin and vanilla for about 2 to 3 minutes on medium speed.
Stir the flour mixture into the egg mixture, then mix in the cooled pecans (the mixture will be crumbly).
On a lightly floured work surface, divide the dough in half. Shape each half into a 3×10-inch log. Set the logs lengthwise on the prepared baking sheet, evenly spacing them apart.
Dampen your hands and smooth the surface of the logs. Bake in preheated oven until the logs are slightly firm to the touch, about 25-30 minutes.
Remove the baking sheet from the oven and decrease the oven temperature to 300 degrees. Let the logs cool on the baking sheet for 15 minutes.
Transfer the logs to a cutting board. With a serrated bread knife, cut each log diagonally into slices ½ inch thick.
Place the cookies, cut sides up, in a single layer on the baking sheet. Bake until the biscotti are firm, about 20 minutes, flipping them midway through baking. Let cool completely. Once the biscotti is completely cool, melt the white chocolate chips and drizzle over the cookies. Store in an airtight container for up to one week. If you want to freeze the biscotti, I recommend not adding the white chocolate until you are ready to serve them. Story in a freezer-safe container in the freezer for up to 2 months.