Cook the somen noodles according to package instructions, then rinse under cold water and drain well.
In a bowl, mix the dashi, soy sauce, mirin, and sake to make the dipping sauce.
Chill the dipping sauce and cooked noodles in the refrigerator.
To serve, place the cooked somen noodles on a plate and top with sliced cucumber, cherry tomatoes, shredded nori, soft-boiled egg, and grilled chicken.
Pour the chilled dipping sauce over the noodles and serve with ice cubes on the side.
