A couple of hours beforehand, put the butter in a small pan and heat it until it bubbles. Use a whisk to scrape the base and sides of the pan, so the milk solids don’t burn. From the moment the butter melts, it should take 3-4 minutes over a medium heat. Have a bowl ready to tip the brown butter into. It will start smelling like butterscotch, its colour changing from light gold to amber, and its bubbling sound will quieten. Pour it into the bowl.
Whisk the miso into the warm butter; you should have 225g of butter mix. Put it into a container and leave it to cool and firm up (stir it a couple of times while it sets, to re-emulsify). You want it to be soft, like room-temperature butter.
Preheat the oven to 170°C Fan. Line a 20cm square or round cake tin, or a 900g loaf tin, with baking parchment.
Put the cooled brown butter-miso mix in a mixing bowl, or the bowl of a food mixer, together with the sugar. Beat for 5 minutes with electric beaters or the food mixer at a high speed. (If you’re doing it by hand, beat it for a little longer.)
Beat the eggs one at a time into the mixture, scraping down the bowl in between each. Add the self-raising flour and fold it in carefully by hand with a spatula. This bit will feel weird – to add yogurt at the end, after the flour – but don’t worry. It works. So mix in the yogurt, again by hand. Spread the batter into the prepared tin, scatter the walnuts over, then push them into the batter slightly
Bake for 40-50 minutes, or until a skewer comes out clean. Leave to cool.
While it is cooling, in a pan dissolve the sugar in the measured water. Take it off the heat, add the miso and whisk it all together. Add the chopped walnuts and put the pan back over the medium heat for a couple of minutes, stirring the whole time. Spread the syrup over the cake, let it cool slightly, then enjoy.