Start by preheating your oven to 350°F (175°C). Grease a 9-inch round cake pan and line the bottom with parchment paper—this will make it super easy to pop the cake out later.
In a big mixing bowl, toss together the flour, baking powder, salt, sugar, and chopped walnuts. Stir it all up so that the walnuts get coated in the dry mix and don’t sink to the bottom of the cake.
In another bowl, mash the bananas until they’re smooth and creamy. Add the eggs and oil, and give it all a good whisk until it’s well combined.
Pour the wet mixture into the bowl of dry ingredients. Stir it gently—don’t overmix, just enough to combine everything. Now fold in the grated carrots until the batter looks evenly mixed and vibrant.
Spoon the batter into your prepared pan, smoothing the top with a spatula. Slide it into the oven and bake for about 40–45 minutes. You’ll know it’s done when the top is golden and a toothpick inserted into the middle comes out clean. Let it cool in the pan for 10 minutes, then transfer it to a wire rack to cool completely.
While the cake cools, beat the cream cheese and softened butter together in a bowl until silky smooth. Gradually add the sifted confectioners’ sugar and vanilla extract, mixing until you have a creamy, spreadable frosting.
Once the cake is cool, spread the frosting generously over the top. Use the back of a spoon or a spatula to swirl it around for a rustic look. Top it off with walnut halves for a simple but classic finish.