Preheat the oven to 350 degrees. Combine the flour, cinnamon, baking powder, and salt in a large bowl. In a separate bowl, whisk the egg, oil, and sugar until fully combined. Slowly fold the flour mixture with the egg mixture and stir a few times (like 5 or less around the bowl). Fold in the carrot and walnut.
With nonstick spray, lightly grease a small baking vessel, ramekin, or muffin tin. Scoop the batter into the baking vessel. Bake for 15 to 25 minutes until a toothpick inserted into the center comes out clean. Let cool before icing.
For the frosting, blend the cream cheese, powdered sugar, and vanilla until smooth.
Spread the icing on and portion before serving.