To make the peanut dressing, put the peanut butter in a large bowl, and using a whisk, combine the warm water to loosen the peanut butter.  Continue to add the ingredients in the order listed, whisking well after each addition to thoroughly combine.  Taste for seasonings and adjust, if necessary.

Bring a large pot of salted water to a boil over high heat.  Cook the noodles, stirring occasionally, according to the package directions (about 4 to 5 minutes).  Drain in a colander and rinse under warm water.  Drain well before adding to the peanut dressing.

In a large skillet, heat the 1/4 cup peanut oil over medium-high heat.  Add the mushrooms, stirring to coat with the oil.  Leave the mushrooms untouched to allow to caramelize.  When the mushrooms begin to release their liquid, sprinkle with salt and turn the heat up to high; cook until softened and golden brown, about 12 to 14 minutes total.  Add the mushrooms and bean sprouts to the noodles and toss to combine.  Garnish with peanuts and cilantro.  Serve warm, at room temperature, or chilled.