1. PREHEAT the oven to 350°F. Lightly butter three 8-inch round cake pans. Line the pan bottoms with parchment paper (we like these the best—the pre-cut parchment rounds have handles for easy removal of the cake layer). Dust the insides with flour and tap out the excess.
2. SIFT together the flour, baking soda, baking powder, cinnamon, ginger, nutmeg and salt in a medium bowl.
3. BEAT until foamy, in a large bowl with an electric mixer—on high speed, the granulated sugar, oil and eggs (about 1 minute). Reduce the mixer speed to low. In thirds, beat in the flour mixture, alternating with two additions of the pumpkin. Mix, scraping down the sides of the bowl as needed, just until smooth. Spread evenly into the cake pans.
4. BAKE the layers until a wooden toothpick inserted in the center of a cake comes out clean, 25 to 30 minutes. Let cool in the pan on wire cake racks for 10 minutes (check out this three tier cooling rack). Run a knife around the inside of each pan and invert onto a rack to unmold the cake. Remove the parchment paper and turn right side up. Let cool completely. (The cakes can be individually wrapped in plastic wrap and stored at room temperature for up to 2 days.)
5. MAKE the brandied cream: Use a medium bowl and an electric mixer on high speed to whip together the cream, confectioners’ sugar and brandy. Whip until the mixture is stiff. The cream can be refrigerated for up to 8 hours. If it separates, beat until stiff.
6. ASSEMBLE. Set one-third of the raspberries aside to garnish the cake. Using a small knife, split the remaining raspberries down their sides so they can be opened flat. Put one cake layer on a serving plate. Spread with one third of the cream and add one-half of the split berries. Add a second layer and repeat with another third of the cream and the remaining split berries. Top with the last layer of cake and remaining cream, garnish top with the reserved raspberries. The assembled cake can be refrigerated for up to 2 hours (then the whipped cream starts to deflate). Serve chilled.