Bring a large pot of salted water to a boil and cook the pappardelle according to package directions until al dente. Reserve 1/2 cup of pasta water, then drain the pasta.
Melt the butter in a large skillet over medium heat. Add the shallot and cook for 2 minutes until softened.
Stir in the garlic and cook for 1 minute until fragrant.
Add the sliced mushrooms and thyme leaves. Cook for 6 to 8 minutes, stirring occasionally, until the mushrooms are browned and their liquid has evaporated.
Pour in the heavy cream and bring to a gentle simmer. Season with salt and black pepper.
Add the drained pasta and Parmesan cheese to the skillet. Toss to coat, adding a splash of reserved pasta water if needed to loosen the sauce.
Remove from heat and sprinkle with chopped parsley before serving.