Preheat an oven to 350 degrees F (175 degrees C). Place an 8- or 9-inch cast iron skillet into the oven to preheat. Whisk together the flour, white sugar, brown sugar, salt, cinnamon, nutmeg, and cloves in a bowl; set aside.
Beat together the eggs, vanilla extract, and melted butter in a mixing bowl. Toss the apples and pecans in the flour mixture, then stir into the egg mixture until combined. Melt 1 tablespoon of butter in the preheated skillet, swirling to coat the pan.
Pour the batter into the hot pan, and replace into the oven. Bake until the sides are dry and a toothpick inserted into the center of the brownie comes out clean, about 40 minutes. Cool in the skillet 20 minutes before removing and slicing.