Prepare the flax egg by mixing together the flaxseed and water in a small bowl. Set aside.
In a medium mixing bowl, sift together the flour, baking powder, baking soda, salt, nutmeg, and cinnamon.
Add the carrot and brown sugar.
Mix the remaining ingredients in. Wait to add the almond milk as you may not need it. If your carrots release a lot of liquid it should work without, but generally, we need to add some.
Allow the mixture to sit for a couple of minutes. At this point, grease or line a muffin pan with liners.
Scoop the batter into the liners going about ¾ full, leaving enough room for them to rise.
Bake for 20-22 minutes (when a toothpick comes out clean).
Remove from heat and allow to cool to room temperature before frosting.
Cashew Frosting
To make the frosting, once the nuts have been soaked, add everything to a food processor or high-speed blender and blend on high until it's finely ground. I found the blender gets the particles finer than the processor.
Once the cupcakes are cooled, spread or pipe on to cupcakes.
Once frosted, they can be kept for up to 1 week in the fridge, or 2 days at room temperature.