Preheat the oven to 375F, and spray a regular sized loaf pan with nonstick cooking spray.
In a bowl, whisk together your eggs and brown sugar until it’s light and fluffy.
Stir in the yogurt, applesauce, and vanilla extract.
Mix in the all purpose flour, baking powder, baking soda and spices.
Fold in the carrots.
Pour the batter into the loaf pan and bake it in the oven for 45-50 minutes- until baked all the way through.
Let it cool before removing from the pan.
To make the icing, mix the cream cheese, icing sugar, butter, and vanilla together until creamy. Spread the icing on the loaf then sprinkle with walnuts. Makes 10 slices.