Preheat oven to 325 degrees and line one large baking sheet with parchment paper. Combine flour, baking powder, salt, and pumpkin pie spice until well mixed. Set aside. For the pumpkin spice topping: whisk granulated sugar with pumpkin pie spice in a small bowl and set aside until ready to use.
In the bowl of your stand mixer (or a large bowl with a hand mixer) beat pumpkin puree and both sugars until well incorporated. Beat in egg and egg yolk, followed by vanilla. On the lowest speed, mix flour mixture into pumpkin mixture until dough comes together (it will be super sticky! That is ok!).
Divide dough in half and shape each half into a log, approx 9 inches by 1 1/2 inches. I do this (with a great deal of patience) by putting it between two pieces of plastic wrap and gently shaping it, removing one piece of the plastic wrap, and then flipping it over onto the cookie sheet.
Leave approximately 2 inches between both logs, then brush with beaten egg and sprinkle generously with pumpkin spice topping.
Bake at 325 for 40-45 minutes. Remove and let cool for 10 minutes before gently slicing on the diagonal with a serrated knife. Place sliced biscotti cut side down on baking sheet, sprinkle with rest of pumpkin spice topping, then bake again at 325 for 15-20 minutes, or until the biscotti are no longer soft in the middle. Let cool completely on a wire rack.