Bring a large pot of salted water to boil over high heat. Add the linguine and cook 1 minute shy of al dente. Drain, reserving 1 cup of pasta cooking water. Transfer the pasta back to the pot and set aside.
Mushrooms: Preheat the oven to 425°F. Spread the mushrooms evenly on a large baking sheet. Bake until the mushrooms shrink considerably, 5 to 8 minutes.
Combine the tamari, oil, and paprika in a small bowl, mixing well. Add the mixture to the mushrooms and stir well. Spread the mushrooms out as much as possible and continue to bake until almost crisp, about 15 minutes, stirring midway through baking.
Sauce: Combine the cashews with enough water to cover in a small saucepan. Cover the pan, bring to boil, reduce to simmer and cook for 5 minutes. Remove from the heat and set aside for 5 minutes.
Drain the cashews, rinse well and transfer to a blender. Add the water, garlic, and miso. Blend until smooth.
Assembly: Heat the pasta over medium heat and add the wine and cashew mixture, stirring well. Cook until the sauce thickens, about 2 minutes. Add the spinach, ½ cup of the reserved cooking water, and peas. Stir well and cook until the spinach wilts, about 2 minutes.
Add more pasta water a little at a time if the sauce is too thick. Taste and adjust seasoning. Serve the pasta in shallow bowls, garnished with lots of black pepper, scallions, mushrooms, and black salt, if using.