Preheat oven to 350F and line an 8x8-inch square baking dish with parchment paper.
Blend the drained cottage cheese until smooth.
Add the eggs, melted coconut oil, and vanilla to the blended cottage cheese and blend again until combined.
Transfer to a large bowl. Add the almond flour, coconut flour, caster sugar, baking powder, cinnamon, and salt. Stir until just combined. The batter will be thick.
Fold in 1 cup finely shredded carrot, reserving a tiny amount for sprinkling on top.
Spread the batter evenly into the prepared baking dish.
Bake for 30-35 minutes, until the center is set and a toothpick inserted into the middle comes out clean.
Let cool completely.
Beat or whisk the softened cream cheese, Greek yogurt, and maple syrup until smooth and creamy.
Spread the frosting evenly over the chilled carrot cake.
Sprinkle the reserved shredded carrot over the top.
Slice into 12 bars and keep refrigerated until ready to serve.