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Heat the olive oil in a large, deep skillet or Dutch oven over medium heat. Add the onion, carrot, and celery and cook until the vegetables have softened but not browned, about 5 minutes. Add the garlic and cook for 1 minute more.
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Add the lamb and cook, breaking up large chunks with a wooden spoon, until the meat is browned and most of the liquid has evaporated, 5 to 10 minutes (it's OK if there are still some lamb juices in the pan).
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Add the salt, pepper, Italian seasoning, and tomato paste and stir to combine. Pour in the red wine and cook until it has reduced by half, 2 to 3 minutes. Stir in the crushed tomatoes and bring to a boil. Reduce the heat, add the rosemary spring, and simmer until the sauce has thickened and darkened slightly in color, and the flavors have blended, 20 to 30 minutes. Remove and discard the rosemary sprig. Serve over pasta, polenta, or hearty Italian bread.