Cook the pasta in a large pot of boiling, salted water according to package directions.
Drain well, return to the hot pot, and cover to keep warm.
While the pasta cooks, heat the olive oil in an extra-large skillet over medium-high heat.
Add the sliced mushrooms and minced garlic.
Cook for 5 to 8 minutes, stirring occasionally, until the mushrooms have released their liquid and are tender and browned. If they brown too quickly, reduce the heat. Use a slotted spoon to transfer the cooked mushrooms to a bowl and cover to keep warm.
In a separate medium bowl, whisk together the vegan sour cream, all-purpose flour, smoked paprika, and black pepper until no lumps remain. Gradually whisk in the vegetable broth until the mixture is completely smooth.
Pour the sour cream mixture into the same skillet used for the mushrooms.
Cook over medium heat, stirring constantly, until the sauce thickens and begins to bubble.
Continue to cook and stir for 1 minute more.
To serve, spoon the mushroom mixture and creamy sauce over the warm pasta.
Garnish with fresh parsley, if desired.
