Preheat oven to 350*F.
Combine flour, brown sugar, baking powder, salt, and pumpkin pie spice in a large bowl; stir well. In another bowl, combine pumpkin, eggs, and vanilla, stirring well with a wire whisk. Slowly add pumpkin mixture to flour mixture, stirring until dry ingredients are moistened. (Mixture will be very crumbly; it will gradually become moist after stirring.)
Melt butter in a large skillet over medium heat; add nuts. Cook, stirring constantly, until nuts are browned. Remove from heat and cool completely.
Knead or gently stir cooled nuts into dough. Place dough on a lightly floured surface and divide into 2 portions. Lightly flour hands and shape each portion into a 2 x 10″ long log. (Or I just made one large 8″ x 16″ log.) Place logs 3″ apart on lightly greased cookie sheet. Bake for 24 minutes; cool logs 15 minutes. Reduce oven temperature to 300 F.
After some cooling, move a loaf to a cutting board and cut diagonally into 1/2″ thick pieces. Do the same to the other loaf. The interior of each biscotto should still be just a little moist (while the exterior is nice and hard). The crust of the loaf will probably be quite hard, so use a large serrated knife such as a bread knife for this job.
Place the biscotti with a cut side facing up on a half sheet pan and bake for 8 minutes. Remove the pan and flip all the biscotti over so the other cut side is now facing up. Bake for another 7 minutes. Set all the pieces on a wire rack to cool making sure that none of the biscotti are touching each other. If the biscotti are placed too close together, they could get a little soft or soggy as they cool.
Once the biscotti have fully cooled, they can be consumed as is, or white chocolate dipped or drizzled. To melt the chocolate, pop it in the microwave and heat for 30 seconds, then stir. Then continue heating in 15-second increments (carefully) and stirring in between until chocolate is melted. (I usually add in a little shortening to help it melt and avoid burning.) Then just dip a fork in the chocolate and swish it over biscotti to drizzle, or you can pour it in a Ziplock or pastry bag (with a tiny corner snipped out) and squeeze it out.
The biscotti tastes best during the first few days, but will keep for up to a month in a sealed air-tight container.
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