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, and mushrooms, 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 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 the sauce has thickened, about 5 - 7 minutes. Once the sauce has thickened up a bit, stir in the yogurt and parmesan.
Add the pasta and toss to combine. Taste and add more salt and pepper if desired.
Serve immediately and garnish with thyme, cracked pepper, and additional parmesan.
Notes
** to time everything correctly, I recommend starting to cook the pasta when you add the vegetable broth into the sauce.