Preheat your oven to 350℉. Line an 8x4 inch loaf pan with parchment paper.
To a blender or food processor, add the ingredients of the bread - EXCEPT the shredded carrot and walnuts. Pulse this until mostly smooth. Then stir in the carrot and walnuts with a spatula. Pour this mixture into your pan and bake for 35-40 minutes. Or until toothpick comes out clean. Let the bread set in the pan for 20 minutes then transfer to a cooling rack and allow to cool completely for the frosting.
Frosting:
Add all frosting ingredients to a small bowl and whisk until smooth. Spread the mixture on top of the cool loaf atop with some crushed walnuts.