Place soy sauce in a saucepan over medium heat, add brown sugar and bring to a boil. Turn heat to low, stir in molasses, and return to simmer. Transfer to a mixing bowl. Add sesame oil, tahini, chili oil, and vinegar, and whisk to combine. Season to taste with salt, if desired.
Bring a large pot of salted water to a rapid boil. Add noodles, bring back to a boil, and cook, stirring occasionally, until they just begin to soften, about 3 minutes. (Soba noodles can overcook very quickly, so stay nearby.)
Have ready a large bowl of iced water. Drain noodles, plunge in iced water, and drain again. Place in a colander and rinse well under cold running water. Combine noodles and sauce, toss well with scallions, and chill. Serve in small nests on lettuce-lined plates with Chopped Tofu and Parsley.
c.1997, M.S. Milliken & S. Feniger, all rights reserved