In a bowl, cover the oxtails with cold water. Let stand 30 minutes. Drain, pat dry, and season both sides with salt and pepper.
In a large skillet, heat olive oil over medium heat. Add oxtails, being careful not to overcrowd the pan, working in batches if necessary. Cook until both sides are nicely browned; transfer to a slow cooker as they finish.
Add the wine to the skillet to deglaze, scraping up any browned bits at the bottom of the pan, then transfer to the slow cooker. Add the vegetables, garlic, herbs and tomatoes with their juices. Season with salt and pepper. Cook on low 6 hours or high 3 hours.
Cool to room temperature. Remove the oxtails to a plate. Skim as much fat as possible from the surface. Puree the vegetables with a blender or immersion blender, or use a potato masher for a chunkier sauce.
Remove the meat from the bones and shred coarsely, then return to the sauce. (This step can be skipped and the oxtails served intact, if preferred).
Prepare the rigatoni according to package directions. Reserve 1 cup of the pasta cooking water before draining. While pasta cooks, reheat the sauce.
When the pasta is cooked and drained, return it to the pasta cooking pot with half the sauce. Bring to a boil, gently tossing to coat the pasta with sauce. Add a few spoonfuls of the cooking water if needed to get the right consistency. Add the cheese, adjust salt and pepper and serve with the extra sauce ladled on top.