Soak your cashew and macadamia nuts for at least 3 to 4 hours, preferably overnight, then drain and rinse before using.
Preheat the oven to 350°F and grease a 9x13 baking pan.
In a large bowl, whisk together the flour, baking powder, baking soda, cinnamon, nutmeg and salt.
In a separate bowl, whisk together the applesauce, almond milk, vanilla, sugar and oil.
Mix the dry ingredients into the bowl with the wet ingredients.
Fold in the carrots and stir until just combined.
Bake for 30 to 40 minutes or until a toothpick inserted comes out clean. Let cake cool completely before frosting.
Make the frosting: combine all frosting ingredients into a high speed blender. 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.
Notes
*Make sure your baking powder is fresh in order for the cake to rise (since there aren't eggs in the recipe). If your baking powder has been in the back of your pantry for too long it may be less effective.
[:br]