In a large bowl, combine the first seven ingredients. In another bowl, beat egg yolks until light and lemon-colored. Beat in honey and orange zest. Stir into dry ingredients just until moistened. Fold in the bananas, carrots and applesauce.
In a small bowl, beat egg whites on high speed until stiff peaks form; fold into batter a third at a time.
Fill greased or paper-lined muffin cups two-thirds full. Bake at 350° for 25-30 minutes or until a toothpick comes out clean. Cool for 5 minutes before removing from pan to a wire rack.
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