Heat peanut oil in small skillet or wok over medium heat. Add ginger and garlic; sauté 1 to 2 minutes. Transfer to large bowl. Add next sesame oil, soy sauce, balsamic vinegar, sugar, chili oil and salt; whisk to blend.
Cook pasta in large pot of boiling salted water until just tender, stirring occasionally. Drain and rinse under cold water until cool. Drain and transfer to bowl with sauce. Add sliced green onions and toss to coat noodles. Let stand at room temperature until noodles have absorbed dressing, about 1 hour. Stir in peanuts and basil; toss . Season to taste with salt and pepper. Serve at room temperature.