Preheat the oven to 350°F. Grease a 9x13-inch baking pan with baking spray or, alternatively, softened butter and flour.
In a large bowl, sift the cake flour, baking powder, baking soda, cinnamon, ginger, cardamom, salt, nutmeg, and cloves through a fine mesh sieve or sifter. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, beat the butter, oil, and brown sugar on medium-low speed until light and fluffy, about 2 minutes. Add the eggs, one at a time, and beat until incorporated, stopping to scrape down sides of the bowl as needed. Add the vanilla and beat until incorporated.
Working in alternating batches, add the flour mixture and buttermilk, mixing in between each addition.
Transfer the batter to the prepared baking dish and bake for about 25 minutes, or until a toothpick inserted in the center comes out clean. Set aside to cool.