Preheat oven to 350. Prepare an 8 x 8 glass brownie pan (or similar size) by wiping surface area with a light coat of oil, and then using a thick strip of parchment paper to line the inside (makes it easier to remove the cake after cooling).
In a large bowl, add flour, almond meal, coconut sugar, baking powder and baking soda (sift in both), cinnamon, salt, and allspice.
In a blender, add mango, banana, maple syrup, milk, lemon juice, and vanilla. Puree until smooth.
Add wet mixture to dry, along with the carrots. Stir until just well combined.
Pour mixture into prepared pan. Bake for 35-40 minutes, until a toothpick or skewer inserted in the centre comes out clean.
Once cool, frost (see below), then let frosting cool, and serve.