Cook the pasta according to the package instructions.**
While the pasta is cooking, prepare the sauce. Heat 1 tablespoon olive oil in a large pan. Add the shallot and saute until golden brown, about 2 minutes. Add the remaining oil, garlic, mushrooms, and thyme, and saute until the mushrooms have softened, about 5 minutes.
Season with a generous pinch of salt and pepper and stir together. Sprinkle in the quinoa flour and saute until everything is coated.
Slowly stir in the vegetable broth, making sure to stir vigorously if any clumps of flour begin to form.
Bring the mixture to a low simmer and cook until sauce has thickened, about 5 - 7 minutes. Once the sauce has thickened up a bit (it will still be quite liquidy!), stir in the coconut yogurt and nutritional yeast.
Add the pasta and toss to combine. Taste and add more salt and pepper if desired.
Serve immediately and garnish with additional thyme, cracked pepper, and vegan parmesan.
* if you don't want to use yogurt, use 1/3 cup of your favorite vegan milk + 1 - 2 teaspoons of lemon juice ** to time everything correctly, I recommend starting to cook the pasta when you add the vegetable broth into the sauce.