Preheat oven to 350°F (175°C). Grease a 9×5 loaf pan or line the bottom with parchment paper.
In a large bowl, whisk together all dry ingredients. Stir in walnuts or coconut if using.
In a separate bowl, whisk together mashed banana, shredded carrot, sweetener, milk, oil, and vanilla until well combined.
Pour the wet ingredients into the dry. Stir until just combined - do not overmix. Batter will be thick.
Pour batter into the prepared pan and smooth the top.
Bake on the center rack for 45 minutes, or until a toothpick inserted in the center comes out mostly clean.
Cool completely in the pan, then run a knife around the edges and invert onto a serving plate.
Once fully cooled, spread frosting on top and garnish with crushed walnuts and shredded carrot.
For the best texture, loosely cover and refrigerate overnight before serving. The bread is even better on day 2 and 3.