Preheat the oven to 350˚F. Line two baking sheets with parchment paper.
Using a standing mixer fitted with the paddle attachment, whip the butter until it turns a pale yellow, about 3 minutes. Add the coconut oil, sugar and orange zest, and continue mixing for another minute. Add the eggs and mix until they're completely incorporated into the batter. Mix in the vanilla extract and pumpkin.
Combine all of the dry ingredients (from the flour through the spices) in a medium bowl and mix thoroughly with a whisk. Fold into the pumpkin mixture in thirds using a spatula. There's no need to go crazy with this, just fold it in until the flour is absorbed. The batter will be fairly thick.
Using a small ice cream scooper (about 1" in diameter) scoop the cookie batter onto the parchment paper, 1" apart. These cookies spread only a little. I can fit 20 scoops easily on a baking sheet.
Bake for 10 minutes, or until the tops are set. Remove and keep on the baking sheet for another minute.
(While the first baking sheet is baking, I set up the second sheet with scoops of batter.)
Cream Cheese Icing
Combine all of the ingredients together in a medium bowl. Using a hand mixer, whip the ingredients together until smooth.
Either pipe or smear icing on the cookies. For an easy way to pipe the icing, put it in a ziplok bag and snip a corner for a piping bag!
I bake one baking sheet at a time on a lower rack (but not the lowest). If you bake two at a time, switch the upper and lower sheets half-way through the baking.