Preheat the oven to 350. Prepare three 8 inch round pans or one 9 x 13 baking dish.
Combine the flour, baking powder and soda, and all the spices together in a large bowl. Chop the crystallized ginger into small pieces. If they get sticky, use a bit of flour to prevent them from clumping together.
Shred the carrots in a food processor and add to the flour mixture. Clean out the food processor.
In the food processor, mix the sugars, orange zest and eggs until smooth. Gradually add the applesauce and oil until it's well combined. Pour the wet batter over the carrots and flour and stir to combine.
Pour into the prepared pans and bake for 30 - 40 minutes. The round pans will be done sooner than the large pan. Cook the cake before removing them from the pans.
Frost the cake with the Orange Cream Cheese Frosting, reserving a ½ cup for the macarons, and place into the fridge for 30 minutes to firm up. This frosting crusted over very nicely.
Fill your Macarons with the reserved ½ cup of frosting. Pipe a large swirl on the cake to attach the macarons to the cake.