Preheat oven to 400F.
Bring a large pot water to a boil over high heat. Generously salt boiling water, add pasta, and cook, stirring occasionally, until al dente (tender but not mushy), about 12 to 15 minutes. Drain and toss with marinara sauce, 1/4 cup of Parmesan, pecorino, and cubed mozzarella in large bowl. Season with black pepper and red pepper to taste; mix to combine. Transfer pasta to an oiled 9- by 13-inch baking dish. Place sliced mozzarella over pasta and sprinkle with remaining Parmesan.
Bake casserole until cheese is lightly browned and hot throughout, about 30 minutes. Serve immediately.
Heat oil in a medium saucepan over medium-high heat; add onion and garlic, and saute until lightly browned, about 3 minutes. Add tomatoes, puree, and herb sprigs; bring to a boil. Reduce heat to low, cover, and simmer for 10 minutes. Remove and discard herb sprigs, stir in 2 teaspoons salt, and season with pepper to taste. Store refrigerated for up to 3 days or freeze for up to 2 months.
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