Preheat oven to 350 degrees. Coat inside of a 9×9″ baking pan with coconut oil, set aside.
In a large bowl, whisk together dry ingredients–flour, cream of tartar, cinnamon, ginger, baking powder, baking soda, and salt. Set aside.
In the bowl of a stand mixer (or with an electric hand mixer), cream together coconut oil and sugar. Add in pumpkin, egg, and vanilla extract. Beat until creamy.
Slowly add dry ingredients to wet ingredients and mix until combined. Press dough into the bottom of prepared baking dish.
Bake for 15-20 minutes, or until toothpick comes out mostly clean. Do not overbake. Remove to a wire rack to cool completely.
Icing
While bars are cooling, prepare icing. Beat together butter and confectioner’s sugar (start with 2 1/2 cups sugar). Add in pumpkin, cinnamon, and ginger. Beat until light and fluffy. Taste it; If more confectioners’ sugar is needed, add 2 tablespoons at a time up to another ½ cup.