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Preheat oven to 350 degrees.
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Pour 1/4 cup of marinara sauce in a casserole dish and spread it out to coat the bottom of the dish.
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Cook rigatoni according to package directions. Drain and toss with 1 1/2 cups of the sauce (until coated nicely).
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Begin layering the rigatoni into the dish as follows: 1/3 of the pasta followed by 1/3 of each of the ricotta and shredded cheese, and 1/4 cup of the grated cheese.
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Pour about 1/3 of a cup of sauce on top of the cheeses and spread it to cover the cheeses. Continue to layer the ingredients in the same order 2 more times, reserving a bit of shredded cheese for the top.
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Top with additional sauce and sprinkle any remaining shredded Parmesan cheese on top.
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Bake for 30 minutes. Allow to sit for about 10 minutes before serving.
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Serve with additional marinara sauce and grated Parmesan cheese.