Preheat the oven to 350 degrees and grease an 8-inch square baking pan.
In a small bowl, stir together the flour, baking powder, cinnamon, nutmeg, and salt. Set aside.
In a large bowl, combine the eggs, butter, maple syrup, and vanilla extract. Stir well, then add the dry ingredients and mix to combine. Stir in the carrots and walnuts.
Bake the cake for 25 to 30 minutes, until the cake is set and a toothpick inserted in the center comes out clean. Cool completely on a wire rack before removing the cake from the baking pan.
While the cake cools, make the frosting. Be sure the cream cheese and butter are well softened. In the bowl of a stand mixer, whip the cream cheese and butter until combined. Slowly add the maple syrup and vanilla extract while beating the mixture. Continue to mix until light and fluffy. You’ll need to scrape down the sides a few times.
Spread the frosting over the cooled cake, and sprinkle with the shredded coconut.