Preheat oven to 350°F. Line your cake pans with parchment paper if necessary and grease well with coconut oil or avocado oil.
In a measuring cup, mix together the dairy-free milk and apple cider vinegar. Let sit for 5 minutes.
1 cup (8 oz) unsweetened almond milk, 1 tablespoon apple cider vinegar
In a large mixing bowl, combine applesauce, coconut sugar, almond milk mixture, nut butter, coconut oil, and vanilla extract. Stir to combine.
½ cup (122g) unsweetened applesauce, ⅔ cup coconut sugar, ⅓ cup (85g) creamy almond butter, ⅓ cup (67g) refined coconut oil, 1 teaspoon vanilla extract
Add oat flour, almond flour, flax meal, cinnamon, nutmeg, baking powder, baking soda, and salt. Stir until combined. Fold in the shredded carrots and nuts.
1½ cup (144g) gluten-free oat flour, 1½ cup (144g) blanched almond flour, 3 tablespoons flax meal, 1¼ teaspoon cinnamon, ¼ teaspoon nutmeg, 2 teaspoons baking powder, 1 teaspoon baking soda, ¾ teaspoon sea salt, 1 cup shredded carrots, ⅔ cup chopped pecans
Divide between two 8" cake pans, or three 6" cake pans (see Notes for other options). Bake for 18 to 22 minutes for the 6" pans, or between 24-28 minutes for the 8" pans. Bake until a toothpick comes out clean. The cakes should spring back when pressed lightly with a fingertip. They will be pretty flat.
Once done, let cool completely on a wire rack before assembling and frosting (directions below).
Store leftovers in an airtight container on the counter for one day, or store the cake in the refrigerator for up to a week.