Preheat the oven to 350-F. Line baking sheets with parchment paper.
In the bowl of a stand mixer fitted with the paddle attachment (or using a hand mixer), cream the butter and the granulated and brown sugars on medium-high speed until light.
Add the eggs and pumpkin puree and mix well on medium speed.
With the mixer on low speed, add the flour, cinnamon, baking powder, cloves, nutmeg, and salt and mix until well blended.
Turn the dough out onto a lightly floured surface; the dough should be soft but not sticky.
If sticky, knead in additional flour.
Divide the dough into 5 equal pieces.
Roll each piece into a loaf about 12 inches long.
Place the loaves on the lined baking sheets, spacing them 4 inches apart.
Bake the loaves for 20 to 25 minutes, or until golden brown.
Cool the loaves on the baking sheets or transfer to a wire rack to cool.
Place the cooled loaves on a cutting board.
Carefully slice the loaves, diagonally, into 1/2-inch-wide slices.
Return the cookies to the baking sheets in a single layer.
Bake the biscottini for 1 another 10 to 15 minutes, or until lightly browned.
Remove the baking sheets from the oven.
Cool the biscottini on the baking sheet.
Stack the biscottini upright for the drizzle.
MAKE THE ICING
Combine the confectioners sugar, water, and cinnamon and mix until smooth.
Using a fork, generously drizzle the icing over the tops of the biscottini.