In a small saucepan, combine the dashi, soy sauce, sugar, sake, and mirin.
Place the pan over medium heat and bring the mixture to a light simmer, stirring until the sugar is fully dissolved.
Remove the sauce from the heat and chill it in the fridge for 2–3 hours, or speed things up by placing the pan in an ice water bath for 15–20 minutes.
Fill a large pot with 3 liters of water and bring it to a boil while you prepare the toppings.
Peel the ginger using the edge of a spoon, then grate it finely.
Peel the radishes (or daikon, if using) and grate them into a small bowl.
Slice the spring onions thinly into rounds.
Quarter or slice the cherry tomatoes into eighths, depending on size.
Halve the cucumber lengthwise, scoop out the seeds with a spoon, and slice into thin matchsticks.
Arrange all of the toppings neatly on a plate or in small bowls, ready for serving.
Gently separate the somen noodle bundles with your hands so they don’t clump when cooking.
Add the noodles to the boiling water and cook according to the package instructions, usually around 3 minutes.
Drain the cooked noodles and rinse thoroughly under cold running water until completely cool and smooth.
Transfer the noodles to a bowl of ice water and let them chill for a few minutes to firm up their texture.
Prepare your table by setting out small dipping bowls (around 80 ml per person), chopsticks or forks, and a draining surface such as a bamboo mat or colander on a plate.
Remove the noodles from the ice bath and place them on your draining surface to serve.
To eat, take a small portion of noodles, dip briefly into the chilled sauce, add your preferred toppings, and slurp away. Refill your dipping sauce if it becomes too diluted.