Preheat the oven to 350°F. Line baking sheets with parchment paper or silpat mats.
In a large skillet over medium heat, melt the butter. Add the nuts and cook, stirring constantly, until the nuts are browned. Remove from heat and cool completely.
In a large bowl, whisk together the flour, brown sugar, baking powder, salt and pumpkin pie spice; stir well to combine.
In a separate bowl, whisk together the pumpkin, eggs, and vanilla.
Slowly add the pumpkin mixture to the flour mixture, stirring until the dry ingredients are moistened. (The mixture will be very crumbly; it will gradually become moist after stirring).
Knead or gently stir the cooled nuts into the pumpkin pie biscotti dough. Place the dough on a lightly floured surface and divide into 4 portions. Lightly flour hands and shape each portion into a 1x15-inch long log. Place the logs 3 inches apart on the prepared baking sheets.
Bake for about 23 minutes. Remove from oven and cool for 15 minutes. Reduce the oven temperature to 300°F. Cut each log diagonally into ½-inch slices using a serrated knife. Place the slices back on the baking sheets. Bake for 15 minutes (flipping the slices over halfway through). Cool completely on wire racks.
ADD THE ICING (optional):
In a microwave safe bowl, heat the white chocolate in 15-second intervals stirring in between until the chocolate is completely melted, about 30 seconds or so. Drizzle over the biscotti. For a nice even drizzle, add the white chocolate to a small bag and snip a small corner to drizzle from.
Notes
*You can also choose to toast the nuts in the oven. Spread nuts in a single layer on a baking sheet. Place in 350 degree oven. Toast until golden (keeping a close eye on them), 10 to 12 minutes. Cool completely.