Cut the rabbit into manageable pieces. Season generously with salt and freshly ground black pepper.
Heat olive oil in a large, heavy-bottomed pot or Dutch oven over medium heat. Brown the rabbit pieces in batches on all sides until deeply golden. Remove and set aside.
In the same pot, sauté the chopped onion, carrots, celery, and minced garlic until softened and fragrant, about 8-10 minutes.
Stir in the tomato paste and cook for 1-2 minutes, allowing it to caramelize slightly. Add the red wine, deglazing the pot by scraping up any browned bits from the bottom.
Add the canned tomatoes, chicken stock, rosemary sprigs, and bay leaves. Return the rabbit pieces to the pot. Bring to a gentle simmer.
Cover and cook over very low heat for 1.5-2 hours, or until the rabbit is falling-off-the-bone tender. Stir occasionally to prevent sticking.
Remove the rabbit pieces from the pot and, once cool enough to handle, shred the meat from the bones. Discard the bones and return the shredded meat to the sauce.
Cook the pasta according to package directions until al dente. Drain, reserving about 1 cup of the pasta water. Toss the pasta with the rabbit ragu, adding a little pasta water if needed to loosen the sauce. Serve immediately, garnished with fresh rosemary or parsley and a drizzle of olive oil.
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