Cream together the butter, sugar, and brown sugar until light and fluffy. Mix in the pumpkin and vanilla until smooth.
In a second bowl, mix together the flour, baking powder, salt, and spices. Mix the wet ingredients into the dry ingredients, until a smooth, thick dough forms. Wrap in plastic and refrigerate 30 minutes.
Heat the oven to 350F; line a cookie sheet with a silicon baking mat. Roll tablespoon portions of dough into round balls, gently flatten between your hand and place 1-inch apart on the baking sheet.
Bake 12-14 minutes, or until the bottoms are golden brown and the tops are just set. Let cool completely.
To make the frosting: In a stand mixer fitted with the paddle attachment, beat the butter until smooth and creamy. Mix in the vanilla bean. Slowly beat in the powdered sugar; mix in the coconut milk. Beat 1 minute, or until thick and fluffy.