Preheat the oven to 170°C (340°F) and toast 100 g (3½ oz) walnuts for 10 minutes. Wrap them in a clean tea towel and scrub the skin in between your hands in the towel. Roughly chop the scrubbed walnuts.
Put 2 tablespoons white miso, 2 tablespoons light brown sugar and 2½ tablespoons mirin in a small saucepan and place over low heat. Keep stirring to a smooth paste.
Scrape the miso mixture into a bowl. Combine with the chopped walnuts. Serve with vegetable sticks or as an onigiri filling.