Adjust an oven rack to the lower third position and preheat the oven to 350 degrees. Butter or coat with cooking spray a 9 by 9 by 2-inch baking pan and dust lightly with all-purpose flour; knock out excess and set the pan aside.
Insert the metal blade into the work bowl of a food processor (standard-size or larger). Put the flour, baking soda, salt, cinnamon, nutmeg, and cloves into the work bowl and process 5 seconds to combine. Transfer to a piece of waxed paper and set aside.
With the metal blade in the work bowl, add the orange zest and brown sugar. Process 15 seconds. Add the egg and vanilla and process for 1 full minute, stopping once to scrape the work bowl.
Add the butter pieces and process about 1 minute, stopping once or twice to scrape the work bowl. The batter should be smooth and fluffy. With the machine running, add the buttermilk through the feed tube and process for 10 seconds. Scrape the work bowl.
Spoon the dry ingredients in a circle on top of the batter. Pulse rapidly 4 times (less than 1 second each), scrape the work bowl gently, and pulse one more time, just until the dry ingredients are incorporated. Do not overprocess; if necessary, stir with the plastic spatula to complete the mixing. The batter may not look completely smooth.
Scrape the batter into the prepared baking pan and spread level. Bake until the top is well browned and springs back when gently pressed in the center, and the cake pulls slightly away from the sides of the pan, about 30 minutes.
Cool the cake in its pan for 5 minutes, then turn it out on a cooling rack. Remove the pan, cover the cake with another rack and invert again to let cake cool completely right side up. Before serving, sprinkle top lightly with confectioners' sugar, if desired.