Preheat the oven to 350°F and grease a 9x13-inch baking pan.

In a large bowl, whisk together the flours, baking powder, baking soda, cinnamon, nutmeg, and salt.

In a separate bowl, whisk together the applesauce, almond milk, vanilla, sugar, and oil.

Add the dry ingredients to the wet ingredients and mix until just combined. Fold in the carrots.

Transfer to the prepared baking dish and bake for 30 to 40 minutes, or until a toothpick inserted comes out clean. Let cake cool completely before frosting.

Make the frosting: In a high-speed blender, place the macadamia nuts, cashews, almond milk, maple syrup, coconut oil, vanilla, lemon juice, and salt. Blend until very smooth, for 1 to 2 minutes or more, scraping down the sides occasionally. You can add an extra tablespoon of almond milk if necessary to get your blade moving.

Chill for at least 30 minutes before spreading. (It will firm up a bit).

Store frosted cake in the fridge.