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Heat a heavy large pot over medium-high heat. Add bacon and sauté until brown and crisp. Drain on a paper towel.
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Sprinkle pork with salt and pepper. Add half of pork to drippings in pot; sauté until brown, about 7 minutes. Set aside. Repeat with remaining pork.
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Add sausage to same pot. Sauté until no longer pink, breaking up with back of fork, about 5 minutes.
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Add onions, carrots, celery, thyme, garlic, bay leaves, and crushed chili flakes.
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Reduce heat to medium-low; sauté until vegetables are tender, about 10 minutes. Add wine and bring to boil, scraping up browned bits.
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Add meat with any accumulated juices; boil 2 minutes. Add tomatoes with juice. Cover and cook until pork is very tender, adjusting heat as needed to maintain gentle simmer and stirring occasionally, about 2 hours.
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Uncover pot; tilt to 1 side and spoon off fat from surface of ragù. Gently press pork pieces with back of fork to break up meat coarsely.
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Season ragù to taste with salt and pepper.
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Preheat oven to 400°F. Butter 15x10x2-inch glass baking dish or other 4-quart baking dish.
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Cook pasta in large pot of boiling salted water until tender but still firm to bite, stirring occasionally. Drain pasta; mix into ragù. Season mixture to taste with salt and pepper; transfer to prepared dish. Sprinkle both cheeses over. Bake until heated through and golden, about 20 minutes.