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Preheat oven to 350°. Grease or line 12 standard-size muffin cups and set aside.
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In the bowl of an electric mixer (or a large mixing bowl), combine the eggs, yogurt, oil, and sugar.
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On medium speed, whisk for one full minute, until the mixture is smooth and thick.
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Add flours, baking powder, baking soda, salt, cinnamon, cloves, and nutmeg to the top of the egg mixture and stir until just combined.
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Add the shredded carrots and mix until evenly incorporated (but don't overmix or they'll be tough!).
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Divide the batter evenly between the twelve prepared cups.
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Bake for 20-25 minutes, until the top of the muffins spring back when lightly pressed. Remove from oven and cool for five minutes before unmolding from the tin.
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Serve warm.