Preheat oven to 350°F and line a large baking sheet with parchment paper.
Combine butter, sugar, spices, baking powder, and salt in a medium bowl until creamy. Once mixture is smooth, add egg and pumpkin puree. Mix the flour into the dough mixture and stir until smooth.
Evenly divide the dough in half and place onto the lined baking sheet. Shape each piece of dough into a log measuring 10 x 2 1/2 inches. Shape them into long rectangles and smooth the tops and sides.
Sprinkle cinnamon sugar over the logs and press into the dough. Note: this step is optional.
Put in the oven and bake for 25 minutes. Remove baking sheet from oven and let cool for about 5 minutes. Reduce oven temperature to 325°F.
Cut the log into 1/2 inch slices crosswise. Use a sharp knife to cleanly slice through the dough. Make sure to cut down as straight as possible to get even pieces.
Place the biscotti pieces on edge on the baking sheet and return to oven and bake for 40 minutes or until they're golden brown. Turn the oven off and crack the door open slightly to allow the biscotti to cool in the oven.
Once completely cool, melt the white chocolate either in the microwave or over the stove. If using the microwave, do only for 30 seconds at a time and stir. If over the stove, it's best to use a double boiler to prevent chocolate from burning.
With the biscotti still on the baking sheet, drizzle the white chocolate over the biscotti. It's easiest to drizzle immediately after the chocolate has melted.
Let the white chocolate harden at room temperature. Store biscotti in an airtight container. To freeze, wrap in parchment paper, followed by aluminum foil or plastic wrap.