Coconut oil's main type of saturated fat, lauric acid, may help boost healthy HDL cholesterol levels.
Preheat oven to 350ºF with racks in upper and lower thirds. Line 2 large baking sheets with parchment. Whisk flours, baking powder, baking soda and salt.
Using an electric mixer on medium speed, blend coconut oil and brown sugar. Beat in pumpkin, eggs and spices. Scrape down sides of bowl; fold in flour mixture.
Drop rounded tablespoonfuls of batter 1 inch apart on prepared sheets. Bake, switching sheets halfway through, until cookies spring back when lightly pressed, 13 to 15 minutes. Let cool slightly on sheets on wire racks, then transfer to racks to cool completely. Repeat with remaining batter.
Whisk cream cheese, coconut cream and confectioners' sugar until smooth. Stir in ginger. Cover and refrigerate until slightly thickened, about 20 minutes. Just before serving, top flat sides of half of cooled cookies with 1/2 Tbsp. ginger cream each. Top with remaining halves and serve.