Preheat oven to 375° F. Cover a baking pan with parchment paper, and set aside.
In a large bowl, add the maple syrup and melted coconut oil. Mix on a low setting with either a stand mixer or hand mixer until creamy. Add the eggs (one at a time) and flax eggs. Beat mixture together until fluffy. Add the vanilla extract, and continue to mix until well combined. Set aside.
In a medium size bowl, add flour, sugar, cinnamon, baking powder, baking soda, salt and cinnamon, and mix until well combined. Slowly add the dry ingredients to the egg mixture, beating on a medium speed until there are no lumps and everything is well combined. Fold in the grated carrots, and pour into prepared pan.
Bake for 40 minutes, or until a toothpick inserted into the center of the cake comes out clean. Remove from the oven, cool in pan for 10 minutes, then turn out onto a wire rack or a plate and cool completely. You could put the cake in the refrigerator to cool quickly before frosting.
Place Icelandic Provisions vanilla Skyr into a small bowl, and beat with a hand mixer until creamy. Frost the cake with the creamy Skyr, and serve.