In a blender, combine tofu, sauerkraut brine, nutritional yeast, miso, cayenne or chile flakes, smoked paprika, black pepper, and vinegar or lemon juice. Blend at high speed, stopping to scrape down sides if necessary, until a very smooth, silky sauce forms. Season with salt. Add ¼ cup (60ml) olive oil and blend in at low speed just until emulsified.
In a large sauté pan, heat remaining ¼ cup (60ml) olive oil over medium-high heat until shimmering. Add mushrooms and cook, stirring, until browned, about 6 minutes.
In a pot of salted boiling water, cook pasta until just al dente. Transfer pasta to pan with mushrooms, reserving pasta-cooking water. Pour on just enough creamy sauce to coat all the pasta, then add about ¼ cup (60ml) pasta-cooking water. Cook over medium heat, stirring, until sauce forms a silky glaze that coats pasta. Serve.
