1. Preheat oven to 350 degrees. Brush two 8-inch round cake pans with butter; line with parchment rounds. Butter parchment; dust with flour, tapping out excess. Whisk together flour, baking powder, baking soda, cinnamon, nutmeg, and salt in a medium bowl.

2. With an electric mixer on medium speed, beat butter and brown sugar until pale and fluffy, 3 to 4 minutes. Beat in eggs, 1 at a time. Beat in pumpkin; add vanilla and ginger. Reduce speed to low. Add flour mixture in 3 batches, alternating with 2 batches of buttermilk; beat until just combined, scraping down sides of bowl as needed.

3. Divide batter evenly between prepared pans. Bake until cakes are golden brown, edges pull away from sides of pans, and a cake tester comes out clean, about 35 minutes. Transfer pans to wire racks to cool 15 minutes. Turn out cakes onto racks to cool completely.

4. Place bottom layer on a cake stand or platter, and spread evenly with half the frosting. Top with second layer, and spread remaining frosting over top. Top cake with some quince-ginger compote, and serve remainder on the side.