Bring a large pot of salted water to a boil. Add the ravioli and cook as the label directs. Reserve 1/2 cup cooking water, then drain.
Meanwhile, heat the olive oil in a large nonstick skillet over medium-high heat. Add the mushrooms and pancetta and season with salt and pepper. Cook, stirring occasionally, until the pancetta is crisp and the mushrooms are lightly browned, 5 to 7 minutes. Stir in the thyme and cook 30 seconds. Add the chicken broth and bring to a simmer.
Add the ravioli and 1/4 cup of the reserved cooking water to the skillet. Bring to a simmer and cook, stirring gently, until the ravioli are coated with the sauce, adding more cooking water as needed. Add the butter and Parmesan and toss until the butter is melted. Stir in the parsley.
Divide the ravioli among bowls. Season with pepper and top with more Parmesan.