Preheat oven to 350°F Sift together the flour, salt, sugar, baking powder, and spices into a large bowl.
In another bowl, whisk together the eggs, pumpkin purée, and vanilla extract. Pour the pumpkin mixture into the flour mixture. Give it a rough stir to generally incorporate the ingredients. The dough will be crumbly.
Flour your hands and a clean kitchen surface and lightly knead the dough. Lightly grease a baking sheet or line it with parchment paper. Form the dough into a large log, roughly about 15-20 inches by 6-7 inches. The loaves should be relatively flat, only about 1/2 inch high. Bake for 22-30 minutes at 350 F, until the center is firm to the touch. (Feel free to also form two smaller logs for cute two-bite biscotti; just cut the baking time to 18-24 minutes.)
Let biscotti cool for 15 minutes and then using a serrated knife cut into 1 inch wide pieces. Turn the oven to 300 F and bake for an additional 15-20 minutes. Cool completely.