Preheat your oven to 350 F. Cover a large baking sheet with wax or parchment paper.
In a large bowl, mix coconut oil and sugars for one minute. Add in pumpkin and vanilla and mix again.
Sift gluten free flour, cornstarch, baking powder and salt. Blend in small amounts into the wet ingredients. If the dough is lumpy, add 1-2 tsp dairy free milk and mix again.
Roll out half of the dough on a floured surface using a floured rolling pin. More flour might be needed to prevent sticking. Dip cookie cutters in flour and use to cut out shapes. Then place the cookies on the sheet prepared earlier. When you have a full sheet, place in the freezer to let dough harden. Repeat until you have used all the dough.
When the cookies are firm, place on another baking sheet and bake 8 minutes or until light golden brown. (If you over bake them they will be too hard). Transfer immediately to a cooling rack after taking them out of the oven. Repeat until you have baked all cookies.
You can eat them plain, OR decorate with frosting.
To make Frosting: In a large mixing bowl, beat softened butter. Add a little powdered sugar at a time until it gets thick. Thin with dairy-free milk to ensure that the frosting is spreadable.