Preheat the oven to 350℉. Line a 9 X 9 inch baking pan with parchment paper. Set aside.
In a small bowl, combine the almond milk and apple cider vinegar and set aside for about 10 minutes, to thicken up to “buttermilk” consistency.
In a large bowl, whisk together the eggs, apple sauce, coconut sugar, avocado oil, maple syrup, vanilla adding the “buttermilk” last.
Sift in the spelt flour, almond flour, baking soda, cinnamon, ginger, nutmeg and salt. Stir until well combined. Fold in the shredded carrots.
Pour into baking pan, and bake for 40 to 45 minutes, or until a toothpick inserted in the middle comes out clean.
Allow to cool on wire rack completely before adding frosting.
Once the cake is completely cooled, prepare the frosting: In a medium bowl, add the cream cheese, yogurt, honey and vanilla. Using a handheld mixer, beat until smooth.
Spread the frosting on top and sprinkle with walnuts or pecans. Cut into 9 squares or 12 smaller squares. Store leftovers in an airtight container in the fridge.