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Preheat the oven to 350°F and line a 8 x 4 loaf pan with parchment paper, leaving an overhang for easier removal.
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In a large bowl, add the eggs, coconut sugar, oil, yogurt and vanilla. Whisk together until smooth.
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In a separate bowl, combine the flour, cinnamon, nutmeg, cloves, baking soda, baking powder and salt. Mix until well combined. Pour the dry ingredients into the wet ingredients and gently stir until almost combined. Gently fold in the shredded carrots until fully incorporated.
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Pour the batter into the prepared loaf pan, smoothing the top evenly. Bake in a preheated oven for 39-46 minutes, or until a toothpick comes out clean. Check on the loaf after 35 minutes. If the top of the loaf is starting to brown really quickly, tent the top of the loaf with a loose layer of aluminum foil for the remaining baking time.
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Remove the pan from the oven and let the loaf cool for 20 minutes then transfer to a cooling rack to cool completely before adding the frosting.
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White the loaf is cooling, beat together all the ingredients for the frosting. Use an offset spatula to spread evenly over the cooled loaf. Sprinkle with chopped nuts. Cut into slices and enjoy.