Preheat oven to 350˚F (180˚C). Line a baking sheet with parchment or lightly grease.
In the bowl of a stand mixer fitted with a paddle attachment or a large bowl, beat the butter, granulated sugar, and brown sugar until light and fluffy. Mix in the eggs, one at a time, followed by pumpkin puree and vanilla extract.
In a medium bowl, combine the flour, pumpkin pie spice, baking powder, and salt. Slowly mix into the butter mixture until just combined.
Divide the dough into 2 equal pieces. Form one of the pieces into a log about 12 inches (30.5 centimeters) long. Place near the edge of the prepared baking sheet and gently flatten until about 3 inches (7.5 centimeters) wide and 1/2 inch (1.25 centimeters) thick. Repeat with other half of the dough.
Bake in preheated oven until set and the bottom is golden brown, about 25 minutes. Remove from oven and allow sit at room temperature for 20 minutes until cool enough to handle.
Use a serrated bread knife to cut each log on the diagonal into 3/4-1 inch (2-2.5 centimeters) thick slices.
Return slices to baking sheet, cut side down. Bake for 10-15 minutes, until the bottom is crisp.
Flip each piece and bake for another 10-15 minutes. Transfer the biscotti to a wire rack to cool to room temperature.
If desired, drizzle one side of the biscotti with melted chocolate and/or white chocolate and optionally cover with sprinkles. Allow to set.
Store the cooled biscotti in an airtight container for up to 2 weeks.