Prep. Preheat oven to 350 F and grease 3 - 8" round cake pans with butter or vegetable oil.
Batter. 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. In a second bowl, whisk together 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). Add dry ingredients to the wet ingredients using your electric mixer until well incorporated. Fold in carrots (3 cups) and pecans (1 cup).
Bake. 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.
Frosting. Combine frosting ingredients in a medium bowl until smooth.
Decorate. Once the cake has cooled to room temperature, frost it. Sprinkle pecans on top, and enjoy!
Notes
Swerve or Lakanto - any brand of erythritol can be used instead, just know they're typically 70% as sweet so adjust accordingly. This batter has only been tested with erythritol, allulose baked goods set differently, so I can't speak to how it will turn out if you swap.
Almond Flour - Use fine grain flour for the fluffiest texture. Best products include Bob's Red Mill, Trader Joe's, or Costco brands.
Whey protein isolate gives our cake fluff. There is no substitute here (other protein powders will not work).
Xanthan gum binds the cake together, don't skip!
Allulose is used in the frosting, as it's not a sugar alcohol based sweetener and won't recrystallize as it sets. You can use powdered erythritol instead, just your frosting will have a slightly crunchy texture.