Dice the carrot, celery and onion. In a large skillet, sauté them in the olive oil until translucent. Chop the lamb into small, bite-sized pieces and add to the vegetables, along with the rosemary, salt, and pepper. Stir together over a medium heat until the meat loses its color. Add the wine and stir together until it evaporates. Add the tomatoes and cook over low heat for about 30-45 minutes, until reduced. Add salt and pepper to taste.
Meanwhile, bring a large pot of salted water to boil. Cook the tagliatelle until al dente. Drain it and add it to the skillet with the sauce. Mix together thoroughly and serve immediately with a sprinkle of Pecorino cheese.