Using whole-milk yogurt yields the best results for this cake. You will need a spring form pan.
Preheat oven to 350 degrees. In a medium bowl, combine the apples, 1/2 cup light-brown sugar, ground cinnamon, and ground cloves, and set aside. Sift together the flours, baking soda, baking powder, and salt into a medium bowl, and set aside. Butter a 9-inch spring-form pan, and set aside.
In the bowl of an electric mixer fitted with the paddle attachment, cream the butter and granulated sugar until light and fluffy, about 4 minutes. Add the eggs, one at a time, until well combined. Add the vanilla extract, and combine. Add the reserved flour mixture and yogurt, and stir just until well combined. Fold in 2/3 of the reserved apple mixture. Spoon half the batter into prepared pan. Sprinkle remaining apples evenly over batter. Top with remaining batter, and smooth with a spatula. Sprinkle top with remaining 1/4 cup brown sugar. Bake until golden brown and a cake tester comes out clean, 1 hour 10 minutes to 1 hour 20 minutes. Cover with foil after 45 minutes of baking. Cool 20 minutes before releasing from the pan.