In a medium pot, bring dashi, mirin and soy sauce to a boil. Set aside to cool; refrigerate until chilled.
Prepare the noodles according to package instructions, drain in a colander, then plunge into ice water to stop cooking. Return noodles to colander. Thoroughly rinse the noodles under cold water to remove excess starch.
Divide noodles into individual portions and place on bamboo trays or regular plates. Pour some sauce into individual dipping bowls (you will likely have some sauce left over), arrange condiments on small plates, and serve with the noodles, letting everyone add condiments to the sauce to taste. Dip small amounts of the noodles into the sauce and eat.
Note: To make dashi, wipe a 4-inch-square piece of kombu seaweed with a damp cloth and soak in a medium pot with 4 cups of water overnight. Remove the kombu and bring water to a boil over medium-high heat. Add 3 tablespoons dried bonito flakes, count 5 seconds, and turn off heat. Once the flakes have sunk to the bottom of the pan, strain out the liquid, discarding the solids.
Recipe Source: This recipe is adapted from Toshio Sakamaki, sushi chef at Ozumo in San Francisco.
The sauce can be modified to taste. Some restaurants add acid, such as rice vinegar or ponzu sauce, to make the sauce more refreshing, while others serve the dish with condiments like wasabi paste, sliced green onions and grated daikon. You can substitute cooked cooked udon noodles for the soba.