Bring a large pot of salted water to a boil. Add the 250g tagliatelle and cook according to package instructions until al dente, about 7-9 minutes. Reserve half a cup of pasta water, then drain the pasta in a colander.
While the pasta cooks, heat 2 tablespoons olive oil and 1 tablespoon butter in a wide skillet over medium heat. Add the finely chopped onion and cook until translucent and soft, about 3-4 minutes. Stir in minced garlic and dried thyme and cook for another 1 minute until fragrant.
Add the sliced mushrooms to the pan. Stir occasionally and cook until they release moisture and start to brown, about 7-8 minutes.
Pour in 1 cup vegetable broth and stir, scraping up browned bits. Let simmer gently for 5-7 minutes until the sauce reduces and thickens slightly. Season with salt and pepper to taste.
Add the drained tagliatelle to the skillet with the mushroom sauce. Toss gently to coat. If sauce is too thick, add reserved pasta water to loosen it.
Remove from heat and sprinkle chopped fresh parsley over the pasta. Add grated Parmesan cheese if desired. Serve immediately.
