Bring a large pot of lightly salted water to a boil. Cook rigatoni in the boiling water, stirring occasionally until tender yet firm to the bite, about 12 minutes.

While the pasta is cooking, puree onion and garlic in the bowl of a food processor.

Heat oil and butter in a medium pan over medium-low heat. Add onion and garlic; simmer until fragrant, about 3 minutes.

Puree tomatoes in the food processor. Add tomatoes to the onion mixture; simmer for 5 minutes. Mix in oregano, parsley, salt, and pepper. Add cooked rigatoni and Parmesan cheese; mix well.

Remove from heat. Toss in mozzarella cheese and let rest for 5 minutes before serving.