1.Preheat the oven to 350°F with the rack in the middle position. Coat a 9-inch springform baking pan with nonstick cooking spray; reserve. (Note: If preparing a classic carrot cake using cream cheese frosting, this cake can be baked in two 9-inch round pans and baked at the same temperature, but for 30 to 35 minutes.)
2. Add the flour, cinnamon, baking powder, baking soda, and salt to the work bowl fitted with the metal chopping blade. Process to sift for 10 seconds. Transfer to a large mixing bowl.
3. Put the walnuts in the work bowl and pulse 2 to 3 times to coarsely chop. Leaving the nuts in the bowl, remove the chopping blade and replace with the shredding disc. Shred the carrots. Add the nuts and carrots to the bowl with the dry ingredients and stir well to fully coat the carrots and walnuts with the dry ingredients.
4. Remove the shredding disc and replace with the chopping blade. Add the sugars to the work bowl. In a large measuring cup, combine the oil, eggs, and vanilla. While the unit is running, gradually add the wet ingredients through the feed tube. Process until well mixed, 30 to 45 seconds, stopping to scrape down the sides of the bowl as needed. Add the wet ingredients to the dry ingredients, and stir until just combined.
5. Pour the batter into the prepared pan. Bake for 1 hour or until a cake tester inserted in the center comes out clean. Cool completely in the pan.
6. Clean the bowl and lid. Prepare either the ice cream or a batch of cream cheese frosting if making a traditional cake. If preparing the classic cake, then assemble a 2- or 4-layer cake and coat with the frosting.
7.If making an ice cream cake, unmold the cake from the springform pan and cut into 3 layers using a serrated knife. Line the springform pan with plastic wrap and then place the bottom layer back in the pan. Top with one layer of the ice cream, then top with one more layer of the cake, followed by another ice cream layer and then the final cake layer. Cover and freeze.
8.Prepare the whipped topping. Put the cream and vanilla in the work bowl fitted with the metal chopping blade. Pulse until the mixture thickens slightly, then add the sugar and salt. Continue with long pulses until very thick.
9.Remove the cake from the freezer and from the pan. Cover the top and sides with the whipped topping, and then returnto the freezer until set.