In a large bowl, combine the yogurt, honey, and eggs, stirring and whisking until well blended. Add the flours, baking powder, and cinnamon, mixing to just combine. Add the oil and stir well to incorporate. Keep stirring until it forms a smooth batter. Stir in the apples. Pour and scrape the batter into a buttered 9-inch round cake pan or a very well-buttered bundt pan.
Bake for about 45 minutes, until the cake feels springy to the touch and a toothpick or cake tester inserted into the center comes out clean.
Cool cake on a rack for about 20 minutes; then turn it out of the pan to cool completely.