1. Preheat oven to 350 degrees Fahrenheit. Prepare muffin pans by spraying with non-stick baking spray.
2. In a large bowl, whisk together flour, almond flour, orange juice, brown sugar, cinnamon, baking powder, salt, and shredded carrots. Set aside.
3. In the bowl of an electric mixer, combine whole eggs and one cup of sugar. Beat on medium-high speed until pale and thick, about three minutes. Gently fold into carrot mixture.
4. In the clean bowl of an electric mixer, beat egg whites on high speed until foamy. Add remaining quarter cup sugar and beat until stiff peaks form, about six minutes. Gently fold the beaten egg whites into the carrot mixture.
5. Pour the batter into prepared muffin pans. Bake for 20 minutes or until a toothpick inserted comes out clean.