Set a large pot of salted water on the stove and cook the pasta according to the package instructions for al dente consistency. Reserve 1/2 cup of the pasta cooking water. Drain the pasta and set aside.
Heat the olive oil and vegan butter in a large skillet over medium-high heat. Add the mushrooms and green onions, sautéing for 5-7 minutes until softened and fragrant.
Stir in the garlic and cook for another 1-2 minutes until aromatic.
Pour in the white wine, allowing it to cook for an additional 1-2 minutes.
Sprinkle the mushroom mixture with flour and toss to coat, ensuring everything is evenly covered.
Slowly pour in the vegan heavy cream, stirring gently to combine. Reduce the heat to low and let it simmer until the sauce thickens slightly.
Add the cooked pasta to the skillet with the sauce, tossing gently to coat the pasta evenly. If needed, thin the sauce slightly with the reserved pasta water.
Remove from heat, then stir in the vegan Parmesan cheese and garnish with parsley. Adjust seasoning to taste with salt and black pepper. Serve hot.