Cook the udon noodles as the label directs; drain and let cool. Meanwhile, cook the edamame as the label directs; drain and let cool.
Heat a grill or grill pan over medium-high heat and oil the grates. Add the scallions and cook, turning, until charred, about 3 minutes. Let cool, then slice.
Make the dressing: Whisk the tahini, soy sauce, vinegar, sesame oil, sugar and ginger in a large bowl. Stir in 1 to 2 tablespoons water to make a smooth sauce.
Add the noodles and edamame to the dressing along with the bean sprouts, carrots and snow peas; toss. Sprinkle with sesame seeds.