Preheat oven to 350 degrees F. Lightly coat three 8-inch cake pans with softened butter. Cut three 8-inch circles out of parchment paper (don't skip this like I did!) and fit them into the bottom of the cake pans. Lightly coat the paper circles with butter and set aside.
Cream butter until smooth in a large bowl with an electric mixer set on medium speed. Add the sugars and mix until smooth. Add eggs, one at a time, beating well after each addition, until the mixture is smooth and light. Set aside.
Combine the pumpkin purée, buttermilk, and vanilla in a medium bowl and set aside. Combine the flour, baking powder, cinnamon, baking soda, and nutmeg in a large bowl and set aside. In thirds, alternately add the flour mixture and buttermilk mixture to the butter mixture, blending well after each addition until smooth.
Pour batter into the prepared pans and bake until a toothpick inserted into the middle of each cake comes out clean -- 35 to 40 minutes. Cool the cakes in the pan on wire racks for 30 minutes. Remove cakes from pans and return to the wire racks until completely cool.
Place one layer on a cake plate and top with one-third recipe of Pumpkin Cream-Cheese Frosting. Repeat with the second and third layers. Serve or store refrigerated for up to four days.