Preheat oven to 300° F. and line a baking sheet with parchment paper. Set aside.
In a medium bowl, whisk together the flour, baking powder, salt and spices. Set aside.
In a large bowl with a hand mixer or the bowl of a stand mixer fitted with a paddle attachment, cream the butter and sugar together until light and creamy, about 2-3 minutes. Add eggs, one at a time, beating well after each addition and scraping down the sides and bottom of the bowl, as needed. Add the vanilla and pumpkin puree and beat well to combine. Add the dry ingredients and mix until well combined.
On the prepared baking sheet, spoon dough into two logs about 3 inches wide by 12 inches long (leaving as much room in between as you can as they will spread a bit). The dough is very moist and sticky, so using moistened hands, shape and smooth the dough as best you can. It doesn't need to be perfectly smooth. Your goal should be just to make it a uniform thickness and width, so it bakes evenly.
Bake in preheated oven for 40 minutes. Meanwhile, make the cinnamon sugar mixture by stirring together the white sugar and cinnamon. Remove from oven (leaving oven on at 300F) and sprinkle warm logs with cinnamon sugar mixture. Allow to logs to cool on the pan for about 10 minutes.
Remove logs to a cutting board and using a serrated knife, cut into 1-inch slices. Return slices to baking sheet, standing them upright on the baking sheet, with a little space between each biscotti. Return to the oven and bake for an additional 15 minutes, then turn the oven off, but leave the biscotti in the oven a further 15 minutes. Remove from the oven, then remove the biscotti to a cooling rack and allow to cool completely.
If desired, top with an icing sugar glaze. Add icing sugar to a small bowl. Add just enough hot water to form a thin glaze. Line cooled biscotti up so they are right up against each other (so the drizzle only goes on top and not down the sides). Drizzle glaze over biscotti and leave to set.
Store biscotti at room temperature in a not-quite airtight container. Biscotti will soften somewhat the longer they sit.
Be sure to read the "Cook's Notes" in the original post, for more tips, options, substitutions and variations for this recipe!