Combine the tahini, soy sauce, vinegar, sugar, sesame oil, ginger, and garlic in a blender and process until smooth. With the motor running, stream in the hot water until the sauce reaches the consistency of heavy cream—it should pour easily but still coat the back of a spoon.

Boil four quarts of water in a large pot and cook the noodles, stirring often to prevent sticking, until they are tender. Drain the noodles and rinse them under cold running water until completely chilled; leave them slightly wet so they don't clump together.

Transfer the noodles to a large bowl and toss with the vegetable oil. Add the radishes, scallions, cucumber, carrot, cilantro, and sesame sauce, then toss until the vegetables are evenly distributed and the noodles are well-coated.

Sprinkle individual portions with sesame seeds and serve immediately while cold.