Bring a large pot of salted water to a boil. Cook pappardelle according to package directions until al dente. Reserve 1 cup pasta water, then drain.
While pasta cooks, heat olive oil and 1 tbsp butter in a large skillet over medium-high heat. Add mushrooms and cook, stirring occasionally, until golden brown and their liquid has evaporated, about 8 minutes. Season with salt and pepper.
Reduce heat to medium. Add remaining 2 tbsp butter, garlic, and shallot. Cook until fragrant, about 1 minute.
Pour in white wine and cook, scraping up any browned bits, until reduced by half, about 2 minutes.
Stir in heavy cream and bring to a simmer. Cook until slightly thickened, about 3 minutes.
Add cooked pasta, Parmesan, and parsley to the skillet. Toss to combine, adding reserved pasta water a little at a time if the sauce is too thick. Season with salt and pepper to taste.
Serve immediately, garnished with extra Parmesan and parsley if desired.
Tips
For best flavor, use a mix of wild mushrooms; if unavailable, cremini mushrooms work well.
The sauce can be made ahead and reheated gently; cook pasta fresh just before serving.
Leftovers can be stored in an airtight container in the refrigerator for up to 2 days.