Preheat your oven to 350°F (175°C). Line an 8x4 inch loaf pan with parchment paper, making sure the paper hangs over the sides for easy removal after baking.
In a blender or food processor, combine the ripe bananas, large eggs, old-fashioned oats, baking powder, pinch of salt, ground cinnamon, vanilla extract, and maple syrup. Blend the mixture until it is mostly smooth, but don't worry about tiny bits—it will give the bread some texture. I find that blending the oats with wet ingredients makes the final loaf extra tender.
Transfer the blended batter to a mixing bowl. Gently fold in the finely grated carrot and chopped walnuts using a spatula, making sure they are distributed evenly throughout the mixture.
Pour the batter into the prepared loaf pan and smooth the top. Bake for 35–40 minutes, or until a toothpick inserted into the center comes out clean. Allow the bread to cool in the pan for 20 minutes, then lift it out using the parchment and transfer to a wire rack to cool completely before frosting.
In a small bowl, whisk together the softened cream cheese, vanilla yogurt, and powdered sugar until the mixture is completely smooth and creamy. This tangy frosting adds a wonderful creamy layer to your bread. I like to taste at this point and add a bit more powdered sugar if I want it sweeter.
Once the bread has cooled fully, spread the cream cheese frosting evenly over the top of the loaf. For a nice finishing touch, sprinkle some additional crushed walnuts if desired. Slice and serve!