Preheat oven to 350 F and grease 3 8" round cake pans with butter or vegetable oil.
In a large bowl, use an electric mixer to beat eggs (4), oil (1 1/4 cups ),erythritol (1 1/2 cups), vanilla extract (2 teaspoons), and apple cider vinegar (4 teaspoons) together.
Add the almond flour (2 cups), whey protein isolate (1/2 cup), baking soda (2 teaspoons), baking powder (2 teaspoons), xanthan gum (1 teaspoon), salt ( 1/2 teaspoon) and ground cinnamon (2 teaspoons). Mix until well incorporated.
Use a rubber spatula to fold in grated carrots (3 cups) and roughly chopped pecans (1 cup).
Pour even amounts of batter into each of the prepared pans.
Bake in the preheated oven for 40 minutes. You'll know the cake is done once the center is set and the top is golden brown.
Allow cake to cool in pans for 10 minutes, then remove the cakes from the pan, and allow them to cool on a wire rack completely.