How to Make It
Light a grill or preheat a grill pan. In a large bowl, toss the mushrooms and scallions with the peanut oil and season with salt and pepper. Grill the mushrooms over moderate heat, turning once, until cooked through and tender, about 4 minutes; transfer to a plate. Grill the scallions, turning once, until softened and blackened in spots, about 2 minutes; add to the mushrooms. Let the mushrooms and scallions cool, then thinly slice them.
In a small bowl, whisk the soy sauce with the ginger, garlic, sesame oil, rice vinegar and chili oil.
In a large pot of boiling salted water, cook the soba noodles until al dente, about 4 minutes; drain. Transfer the noodles to a large bowl. Add the mushrooms, scallions, cucumber and dressing and toss well. Sprinkle with the sesame seeds and serve.