Preheat the oven to 180°C (350°F). Grease and flour a cake pan.
In a large bowl, mix the grated carrots, flours, baking soda, baking powder, cinnamon, nutmeg, and salt.
In another bowl, beat the eggs with the coconut oil or olive oil, milk, and vanilla extract.
Pour the liquid ingredients over the dry ingredients and mix until well combined. Add the chopped walnuts and stir to distribute them evenly throughout the batter.
Pour the batter into the prepared pan and spread it evenly.
Bake in the preheated oven for 30-35 minutes, or until a toothpick inserted into the center comes out clean.
Remove from the oven and let it cool in the pan for a few minutes before transferring to a rack to cool completely.
Meanwhile, if you want to add frosting, mix the Greek yogurt with the honey or maple syrup in a small bowl. Add lemon zest if you want an extra flavor.
Once the cake is completely cool, spread the Greek yogurt frosting on top.
Cut into portions and serve.
Enjoy this delicious sugar-free carrot and walnut cake as a healthy and satisfying dessert!