In a medium saucepan, combine 3 tablespoons of mirin, 3 tablespoons of soy sauce, 1 tablespoon of instant dashi powder, and 3 cups of water. Bring it to a boil over medium heat, stirring gently. Reduce heat and let simmer for 4 minutes before chilling in the refrigerator.

Bring a large pot of water to a vigorous boil. Add the soba noodles and cook for about 4 minutes until tender yet firm. Drain and rinse under cold water to remove excess starch.

Divide the chilled soba noodles into serving bowls. Pour the chilled mentsuyu sauce into dipping bowls and add ice cubes. Garnish the noodles with grated daikon, chopped green onions, and shredded nori, and optionally place a dab of wasabi.

Serve with the dipping sauce on the side. Dip the chilled noodles into the mentsuyu sauce and enjoy.