Bring a large pot of salted water to a boil. Meanwhile, heat the vegetable oil in a medium skillet over medium-high heat. Add the mushrooms and season with salt. Cook, stirring occasionally, until golden and tender, about 4 minutes. Transfer to a large bowl; let cool slightly.
Add the noodles and edamame to the boiling water. Cook until the noodles are al dente, 5 to 6 minutes. Drain and run under cold water until cool; add to the bowl with the mushrooms.
Pulse all but a few cilantro leaves, the mint, scallions, 2 tablespoons water, the soy sauce, vinegar, Sriracha and sesame oil in a food processor until roughly chopped; toss with the noodles and edamame. Top with the remaining cilantro.