Heat the olive oil in a large pot over medium heat. Add the lamb chunks and brown them on all sides for about 6 minutes. Remove the lamb and set it aside.
Add the diced onion and sliced carrots to the same pot. Cook for 5 minutes until the onion softens. Stir in the minced garlic and cook for 1 more minute.
Return the lamb to the pot. Pour in the diced tomatoes and beef broth. Add the rosemary sprigs, salt, and pepper. Bring the mixture to a boil, then lower the heat and cover the pot.
Simmer the stew for 1 hour and 15 minutes, stirring occasionally, until the lamb becomes tender.
While the stew simmers, bring the water to a boil in a medium saucepan. Slowly whisk in the cornmeal. Reduce the heat to low and cook for 15 minutes, stirring often. Stir in the butter and parmesan cheese until smooth.
Remove the rosemary sprigs from the stew. Spoon the polenta into bowls and ladle the stew on top.