Butter a 9-inch square baking pan, then dust with flour.
Sift the cake flour, whole wheat flour, baking powder, salt and cinnamon into a spacious bowl and whisk to blend.
In a separate bowl, whisk together the melted butter, eggs, sugar, brown sugar, applesauce and orange zest.
Add the wet ingredients to the dry and stir to blend.
Finally, stir in the shredded zucchini and walnuts.
Spread the mixture in the prepared pan and bake in the preheated oven for 35 to 40 minutes or until the cake feels firm and springy on top and a toothpick inserted in the center comes out clean. Cool thoroughly before slicing or frosting.
To prepare the frosting, beat the cream cheese and butter with an electric mixer until fluffy.
Add the powdered sugar and beat until smooth, scraping the bowl as needed.
Blend in the vanilla extract and orange juice. Spread over the top of the cooled cake.