Bring a large pot of water to a boil over high heat. Add the soba and reduce the heat to medium. Cook the noodles, uncovered, according to package instructions. Drain in a colander and rinse well in cold water.
Transfer the soba to a baking sheet or plate lined with paper towels and drain until dry. Place in a bowl and refrigerate, covered, until completely chilled.
In a small saucepan, combine dashi, soy sauce, mirin, bonito flakes, and water, and bring to a simmer. Remove from the heat. After five minutes, pass the mixture through a sieve, discard the solids, and chill the sauce in the refrigerator until ready for use.
To serve, divide noodles among serving plates and serve with individual bowls of dipping sauce on the side. Dip small amounts of noodles into the sauce and eat.