Warm oil in a pan over medium-high heat. Sprinkle lamb with salt and cook, turning occasionally, until browned, about 8 minutes. Transfer to slow cooker.
Drain off all but 2 Tbsp. fat from pan. Add onions and carrot; sauté 3 minutes. Pour in wine and bring to a boil, stirring to loosen brown bits at bottom of pan. Transfer mixture to slow cooker. Stir in tomatoes, garlic and rosemary. Cover and cook on low until meat shreds with a fork, 5 to 6 hours. Shred meat and season sauce with salt.
Bring a large pot of salted water to boil. Cook rigatoni until tender, about 10 minutes; drain. Serve rigatoni topped with stew and sprinkle with Parmesan, if desired.
Made this stew - had to add extra broth to keep from getting too thick, but overall delicious. Served the first day over pasta, as directed, and the second day reheated over rice, which in my opinion, was SO MUCH BETTER!!! I would go that route in the future.
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