Preheat the oven to 375°F (190°C) and lightly coat a 9 x 13-inch baking dish with nonstick cooking spray.
Spoon a thin layer of marinara (about 1/4 to 1/3 cup) across the bottom of the prepared dish.
Arrange a single layer of ravioli over the sauce to cover the bottom of the dish.
Spoon 1 cup of the sauce evenly over the ravioli, then sprinkle 1 cup of shredded mozzarella on top.
Repeat layering ravioli, 1 cup sauce, and 1 cup mozzarella until all ravioli are used.
Spread the remaining marinara over the top layer of ravioli and sprinkle with the remaining mozzarella, then evenly scatter the shredded Parmesan.
Cover the baking dish with aluminum foil and bake for 25 minutes (increase to about 30 minutes if using frozen ravioli).
Remove the foil and return the dish to the oven; bake uncovered 5–7 minutes more, until the cheese is melted and bubbly.
Remove from the oven and sprinkle with chopped parsley before serving.