Make the sauce: In a blender or mini food processor, combine the scallions with the rice vinegar, soy sauce, mirin, sesame oil and tahini, and blend or process until fairly smooth. Set aside while you make the stir-fry.
Make the noodles: Bring a large saucepan of water to a boil over high heat. Add the egg noodles to the boiling water, reduce the heat to medium and cook according to the package directions for al dente. Drain.
In a wok or medium saute pan over medium-high heat, heat the oil until shimmering. Add the mushrooms and ginger, and stir-fry until the ginger softens a bit and the mushrooms release some moisture and begin to brown, 2 or 3 minutes.
Add the spinach and stir-fry just until slightly wilted, 1 to 2 minutes. Add the reserved sauce and cooked egg noodles, and stir-fry until everything is coated and warmed through, another 1 to 2 minutes.
Divide between individual shallow bowls and sprinkle generously with the sesame seeds. Serve right away.