Bring a large pot of salted water to a boil. Add the orecchiette pasta and cook according to package instructions until al dente. Drain and set aside, reserving ½ cup of the pasta water.
In a large skillet, heat the olive oil over medium heat. Add the diced onion and sauté for about 3-4 minutes until softened.
Add the minced garlic and sliced mushrooms to the skillet. Cook for an additional 5-7 minutes, stirring occasionally, until the mushrooms are browned and have released their moisture.
Stir in the fresh thyme and cook for another minute. Pour in the vegetable broth and let it simmer for 2-3 minutes.
Reduce the heat to low and stir in the heavy cream. Allow the sauce to simmer for about 2-3 minutes until it thickens slightly. If the sauce is too thick, add a bit of the reserved pasta water to reach your desired consistency.
Add the cooked orecchiette to the skillet and toss to coat the pasta in the sauce. Season with salt and pepper to taste.
Remove from heat and stir in the grated Parmesan cheese until melted and well combined.
Serve immediately, garnished with fresh parsley.