Heat the oven to 350° F. Well grease a springform pan and line with parchment paper. You could also use a square pan, lined with parchment, and two small loaf pans. The parchment will help the cake come out easily.
In a medium bowl, whisk together the flours, spices, baking soda, and salt.
In a large bowl, whisk together the applesauce, oil, and sugar. Add the eggs one at a time, whisking until each is incorporated. Whisk in the pumpkin purée and vanilla extract until very smooth and well combined.
Stir and whisk in the flour mixture and mix just until flour is no longer visible.
Transfer batter to the prepared pan, spreading into an even layer.
Bake until a toothpick inserted into the center of the cake comes out clean, 55 to 60 minutes. Remove from oven and cool for 10 minutes in the pan on a wire rack. Gently flip the cake out onto the rack and cool completely, about 30 minutes.
Make Frosting
In a large bowl with a mixer, cream the cream cheese and yogurt until fluffy. Add the vanilla and the maple syrup one tablespoon at a time. Taste, and add more maple syrup if wished. Spread the top of the cooled cake with the frosting.
Cake will keep, well covered in the fridge, for 3 days.