Preheat oven to 350 degrees F (175 degrees C). Grease 12 muffin cups or line with paper muffin liners.
Sift whole wheat flour, all-purpose flour, baking powder, baking soda, and cinnamon together in a bowl.
Whisk eggs, brown sugar, applesauce, and vegetable oil together in a bowl. Stir egg mixture into flour mixture just until ingredients are moistened; fold in carrots and orange zest. Spoon batter into prepared muffin cups.
Bake in the preheated oven until a toothpick inserted near the center comes out clean, about 30 minutes.
