Heat the olive oil and 1 tbsp butter in a large, deep skillet over medium heat. Add the onion and cook, stirring, until softened, about 3 minutes. Stir in the garlic and a pinch of salt, then add the mushrooms and thyme. Spread into an even layer and cook undisturbed 3 to 4 minutes, then stir and cook until golden and liquid evaporates, about 8 minutes more.

Pour in the vegetable broth, bring to a boil, and scrape up any browned bits. Stir in the pasta, reduce heat to medium, and simmer, stirring occasionally, until pasta is al dente and most liquid is absorbed, about 12 minutes.

Remove from heat and stir in the Parmesan and remaining 1 tbsp butter until melted and glossy. Taste and adjust salt and pepper. Serve in warm bowls with extra Parmesan, parsley, and black pepper.