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Preheat oven to 350 degrees.
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Put 24 cupcake liners in muffin tins.
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In a large bowl, mix the sugars, oil, eggs, applesauce and vanilla together until well combined and there are no lumps of brown sugar.
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Add 1/2 cup of the flour along with the baking powder, baking soda, salt, cinnamon, ginger, nutmeg and cloves. Stir until well incorporated.
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Add the remaining two cups of flour and mix until just combined (but there should be no lumps).
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Fold in the carrots and zucchini.
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Spoon into the cupcake liners, filling about 2/3 full.
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Bake for 18 minutes.