Preheat oven to 350 degrees.
To a large bowl, mix carrots, Greek yogurt, buttermilk, egg whites, vanilla and brown sugar.
Add the self-rising flour, cinnamon, ground ginger and salt and mix until fully combined.
Pour into an 8x8 or 9x9 prepared pan that's sprayed and lined with parchment paper.
Bake uncovered for 45-50 minutes.
While the cake bakes make the frosting. Beat together all the ingredients in a bowl until smooth.
Let the cake cool for 30 minutes before frosting.
Cut into 9 pieces.