Preheat the oven to 340°F and line two 8 inch round cake pans with parchment paper on the bases and lightly grease the sides.

In a large bowl whisk together the gluten free flour, almond flour, ground flaxseed, baking powder, cinnamon, ginger, nutmeg, and xylitol until evenly combined.

Add the grated carrots, chopped pecans, and orange zest to the dry mixture and fold until the carrots are fully coated and evenly distributed.

In a separate bowl whisk the eggs, vegetable oil, and vanilla bean paste until smooth and slightly thickened.

Pour the egg mixture into the dry ingredients and fold gently with a spatula until no dry pockets of flour remain and the batter looks thick and even.

Divide the batter evenly between the prepared pans and smooth the tops with a spatula.

Bake for 28 to 35 minutes, until the cakes are risen, the tops are lightly golden, and a toothpick inserted in the center comes out clean or with a few moist crumbs.

Cool the cakes in the pans for 10 minutes, then run a thin knife around the edges and transfer the layers to a wire rack to cool completely.

For the frosting, beat the softened butter with an electric mixer on medium speed until creamy and pale, about 2 minutes.

Add the powdered xylitol gradually and beat until the mixture is light and fluffy, scraping down the bowl as needed.

Add the cream cheese and orange zest, then beat on low speed just until the frosting is smooth, thick, and spreadable.

Place one cooled cake layer on a serving plate and spread about one third of the frosting over the top in an even layer.

Set the second layer on top and spread the remaining frosting over the top and sides of the cake.

Chill the frosted cake for at least 20 minutes before slicing to help the layers set and the frosting firm up.