Cook the ravioli according to the package directions.
Meanwhile, heat 2 tablespoons of the oil in a large skillet over medium-high heat.
Add the mushrooms and cook, tossing occasionally, until they’re tender and any liquid has evaporated, 4 to 5 minutes.
Add the Swiss chard, garlic, ½ teaspoon salt, and ¼ teaspoon pepper and cook, tossing frequently, until tender, 3 to 5 minutes.
Top the ravioli with the vegetable mixture, drizzle with the remaining oil, and sprinkle with the pecorino.