Line a cupcake pan with 12 liners and then line another with 3 liners.
In a medium-sized bowl, whisk together the flour, cornstarch, baking powder, baking soda, salt, cinnamon, ginger and nutmeg.
In a separate large bowl, whisk together the eggs, brown sugar, cane sugar, vegetable oil, almond milk and vanilla.
Add the dry ingredients to the wet mixture and use a spatula to stir until just combined.
Fold in the grated carrots and let the batter rest for 20 minutes. While it rests, preheat oven to 325F.
Divide the batter into the cupcake liners. They should be 3/4 full.
Bake for 26-28 minutes or until a toothpick inserted into a cupcake comes out clean.
Let cool in the pan for 10 minutes before transferring to a wire rack to cool completely.
For the frosting, add the cream cheese and butter to a mixing bowl and use an electric mixer on medium-high speed to cream together. Gradually add the powdered sugar until the frosting is smooth and creamy.
Frost the cupcakes and top with chopped walnuts (optional).
Store in an airtight container in the fridge for up to 5 days.