Shop-bought ponzu tends to have a slightly harsher citrus flavour, so I recommend making it yourself for this particular recipe. It is a handy condiment to have in the fridge.
Gently toast the sesame seeds in a small frying pan over low heat, shaking the pan from time to time to prevent burning. As soon as you hear the sesame seeds popping, take the pan off the heat and leave them to cool down.
Transfer the sesame seeds to a suribachi or mortar and coarsely grind them.
Cook the udon noodles according to the packet instructions, then drain and rinse under cold running water until cool.
Divide the noodles among four bowls. Mix the chilled ponzu and water together, then pour it over the noodles. Sprinkle the ground sesame seeds over the top and arrange the lime slices over the noodles.
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