Preheat oven to 350ºF (180°C).
Butter and flour (or use baking spray) two 9-inch springform pans (cake pans with removable bottoms). I sometimes use three 7-inch pans. Make certain that the round cake pans fit in your oven and can be baked at the same time.
Sift 2 ½ cups all-purpose flour, 1 teaspoon baking powder, 1 teaspoon baking soda, pinch salt, 1 teaspoon ground cinnamon, ½ teaspoon ground ginger, ¼ teaspoon ground allspice and pinch ground cloves in a bowl and reserve. Or have everything measured and sift them directly over the butter mixture as you add them.
Beat 1 ½ cups unsalted butter for 30 seconds in a large mixing bowl with an electric mixer or in the bowl of a stand mixer with the paddle attachment.
Gradually add 1 cup brown sugar and 1 cup white sugar beating continuously for 3 or 4 minutes, until light and fluffy.
Add 3 eggs, one at a time, beating well after each addition.
Add 1 teaspoon vanilla extract and mix.
Add the sifted dry ingredients (flour mixture) in 3 additions, alternating with ½ cup milk in 2 additions. Beat on low speed until it's all well incorporated, but do not overmix. Use a rubber spatula to scrape down the sides of the bowl a few times so you make sure it's all mixed.
Add 1 ½ cups grated or shredded carrots and 1 apple, grated, and mix just until combined. I use a rubber spatula for this step. Make sure there is no flour or other ingredient that has pooled in the bottom of the bowl. The final batter is smooth and almost slippery.
Pour batter into the prepared cake pans, smooth the top, and bake for about 4o minutes, or until a cake tester or toothpick inserted in the center of the cake comes out clean. It might take more or less depending on the pan size you use.
Let cool completely on a wire rack and then remove.