Preheat the oven to 350°F. Line two 9-inch round cake pans with parchment paper and lightly grease the bottoms and sides.
In a large mixing bowl, beat together 1 stick melted butter, ⅓ cup coconut oil, and 1 cup monk fruit sweetener until well combined. Mix in 1 teaspoon vanilla extract, then beat in 4 eggs one at a time until smooth.
In a separate bowl, whisk together 2 cups almond flour, 1 tablespoon coconut flour, 2 teaspoons baking soda, ½ teaspoon baking powder, 2 teaspoons ground cinnamon, 1 teaspoon ground nutmeg, and ¼ teaspoon salt.
Gradually add the dry ingredients to the wet ingredients, mixing just until combined.
Fold in 2 cups shredded carrots and ½ cup chopped pecans.
Divide the batter evenly between the prepared cake pans and smooth the tops. Bake for 30 to 35 minutes, or until a toothpick inserted into the center comes out clean. Let the cakes cool in the pans for 10 minutes, then transfer them to a wire rack to cool completely.
Frosting
In a large mixing bowl, beat together 16 ounces cream cheese and 1 cup softened butter until smooth and creamy.
Add 1⅓ cups powdered erythritol and 1 teaspoon vanilla extract. Mix on low speed until incorporated, then increase to medium-high speed and beat for 1 to 2 minutes until light and fluffy.
Assemble
Place one cake layer on a serving plate or cake stand and spread a generous layer of frosting over the top.
Place the second cake layer on top and frost the top and sides with the remaining frosting, reserving a small amount for decorating if desired.
Pipe decorative swirls with the reserved frosting and sprinkle the remaining chopped pecans over the top.
Refrigerate the cake until ready to serve. Store leftovers covered in the refrigerator for up to 5 days.
Notes
Refrigerate any leftover cake in an airtight container for up to 5-6 days.