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