Preheat oven to 350F and grease an 8-inch round cake pan, lining the bottom with parchment paper.
Whisk the eggs, melted coconut oil, granulated sugar, brown sugar, and vanilla together in a large bowl.
Stir in the almond flour, cinnamon, nutmeg, baking soda, and salt until a smooth batter forms.
Fold in the grated carrots and chopped walnuts, then pour the batter into the prepared cake pan.
Bake for 35 to 40 minutes until a toothpick inserted in the center comes out clean. Let the cake cool completely.
For the frosting, beat the softened cream cheese and butter until smooth, then mix in the powdered sugar and vanilla. Spread evenly over the cooled cake.