Preheat the oven to 350°F. Grease and line an 8x8 baking pan with parchment and set aside.
Whisk together the flaxseed meal and water in a small bowl. Set aside for 5 minutes.
Meanwhile, blend the chickpeas, banana and applesauce in a food processor until completely smooth.
In a large mixing bowl, whisk together the dry ingredients, reserving the hemp hearts, carrot and walnuts. Pour the chickpea puree into the bowl along with the flax egg and mix to combine.
Fold in the hemp hearts, grated carrot and walnuts.
Dump the batter into the prepared pan. Bake on the center rack for 22 - 26 minutes until a toothpick inserted into the center comes out clean.
Let cool in the pan for 10 - 15 minutes, then transfer to a wire rack and cool completely before frosting and slicing.
Slice into 12 - 16 bars. Store in an airtight container for 2 - 3 days.