Preheat and prepare. Set your oven to 180°C (160°C fan)/350°F. Grease a 20cm (8-inch) square baking tin and line it with a strip of parchment paper, leaving an overhang on two opposite sides to act as handles. The room will start to feel warm and inviting.

Whisk the dry ingredients. In a medium bowl, whisk together the flour, bicarbonate of soda, baking powder, salt, and cinnamon. The cinnamon will release its earthy, sweet scent as you whisk. Set this bowl aside.

Cream the butter and sugars. In a large bowl using a stand mixer or hand mixer, beat the 115g of softened butter with the golden caster sugar and light brown sugar until pale, light, and fluffy. This takes about 3-4 minutes. You’ll see the mixture become airy and hear it change from a slapping sound to a softer, smoother rhythm.

Add the eggs and banana. Beat in the eggs one at a time, ensuring the first is fully incorporated before adding the second. Add the vanilla extract. The batter will look smooth and glossy. Now, fold in the mashed banana using a spatula. Don't worry if the batter looks a little curdled at this point – it's perfectly fine and the texture of the banana will ensure a moist cake.

Combine wet and dry. Gently fold half of the flour mixture into the wet ingredients until just a few streaks of flour remain. Pour in the buttermilk and fold again. Finally, add the remaining flour mixture and fold until no dry pockets remain. Stop as soon as it comes together; the batter should be thick, creamy, and smell wonderfully fruity.

Bake the cake. Pour the batter into the prepared tin and smooth the top with a spatula. Bake for 45-50 minutes. The cake is ready when a skewer inserted into the centre comes out clean or with a few moist crumbs. The top should be a deep golden brown, and the edges will have pulled slightly away from the sides of the tin. A wonderful, sweet banana aroma will fill your kitchen. Let the cake cool in the tin for 15 minutes, then use the parchment overhang to lift it onto a wire rack to cool completely.

Make the brown butter frosting. While the cake cools, place the 115g of butter for the frosting in a small, light-coloured saucepan over a medium heat. Melt the butter, then continue to cook, swirling the pan occasionally. First, it will foam, then the milk solids at the bottom will turn from pale yellow to a deep, nutty brown. You'll smell a distinct, toasty, hazelnut-like aroma. As soon as it reaches a deep amber colour and the aroma is intense, remove the pan from the heat and pour the butter into a heatproof bowl (including all the brown bits at the bottom). Allow it to cool until it is just warm to the touch, about 10-15 minutes, but still liquid.

Finish the frosting. Add the sifted icing sugar, 2 tablespoons of milk or cream, and the vanilla extract to the cooled brown butter. Beat with a hand mixer on low speed until combined, then increase to high speed and beat for 2-3 minutes until light, fluffy, and spreadable. If it’s too thick, add the remaining tablespoon of milk. If it’s too thin, add a little more icing sugar. The frosting should be silky and glossy.

Frost and serve. Once the cake is completely cool, spread the brown butter frosting evenly over the top. For a decorative touch, create swirls with the back of a spoon. Sprinkle with a pinch of flaky sea salt if using. Slice and serve.