Cook the Pasta: Bring a large pot of salted water to a boil and cook the pasta according to package instructions until al dente. Drain and set aside, reserving about 1 cup of the pasta water.
Sauté the Aromatics: In a large skillet, heat the olive oil over medium heat. Add the chopped onion and sauté until translucent, about 5 minutes. Stir in the minced garlic and cook for an additional 1-2 minutes, until fragrant.
Add the Mushrooms: Toss in the sliced mushrooms and cook for about 7-10 minutes, stirring occasionally, until the mushrooms are browned and have released their moisture.
Season: Sprinkle in the dried thyme, smoked paprika, salt, and black pepper. Mix well to combine and let the spices marry with the mushrooms for another minute.
Make the Flour Mixture: Add the flour to the mushroom mixture and stir to coat the mushrooms evenly. Cook for 1-2 minutes, allowing the flour to toast slightly.
Deglaze: Pour in the vegetable broth and soy sauce, scraping the bottom of the pan to release any flavorful bits. Bring the mixture to a simmer and let it thicken for about 3 minutes.
Create the Creamy Sauce: Once thickened, lower the heat and stir in the coconut milk and nutritional yeast (if using). Allow the sauce to simmer for another 2-3 minutes until creamy. If the sauce is too thick, you can add some reserved pasta water to reach your desired consistency.
Combine: Add the cooked pasta to the mushroom sauce, gently tossing until the pasta is well-coated. Adjust seasoning if necessary.
Serve: Ladle the stroganoff into bowls and garnish with freshly chopped parsley. Enjoy warm!