Prepare the Oven and Baking Tin: Preheat the oven to 350°F (175°C) and line a loaf tin with baking parchment.
Mash the Bananas: Mash the three ripe bananas with a fork until mostly smooth.
Add the Eggs and Wet Ingredients: Stir the eggs, maple syrup and vanilla extract into the mashed bananas until evenly combined.
Combine the Dry Ingredients: Mix the rolled oats, baking powder, cinnamon and salt in a separate bowl.
Prepare the Carrot and Walnuts: Finely shred the carrot and chop the walnuts into small pieces.
Build the Batter: Fold the dry mixture, carrot and walnuts into the banana mixture until no dry oats remain.
Fill the Baking Tin: Transfer the batter to the prepared loaf tin and spread it evenly.
Bake Until Set: Bake at 350°F (175°C) for 35–40 minutes, until the loaf is set and gently springy in the centre.
Cool the Loaf Completely: Cool the loaf in the tin briefly, then transfer it to a wire rack and cool completely before frosting.
Prepare the Frosting and Finish: Beat the cream cheese, vanilla yoghurt and icing sugar until smooth, spread over the cooled loaf, then slice and serve.