For the chilled noodle soup, put all the ingredients of the soup in a pot. Bring to simmer, and cook for 5 minutes over low heat. Strain the soup into a bowl and discard the kombu seaweed and bonito flakes. Chill the soup in a refrigerator completely.
Bring a large pot to boil for the noodle. Cook the udon noodle according to the instruction of the package. Drain the pot and rinse the noodle with ice water. Once the noodle is chilled, strain it completely.
Divide the noodle into two serving bowls and pour the chilled noodle soup. Top with cucumber, cherry tomatoes, radish, salad mix, tuna, radish sprout, and green onion. Drizzle mayonnaise and sprinkle toasted sesame seeds.