Soak the lentils in cold water for at least 4 hours. Chop the onions, celery and carrots into a small dice. In a large skillet, over medium heat, saute the vegetables in olive oil. When translucent, add the tomato puree and rosemary, and cook together for a minute or two. Add the lentils, and cook together for a minute or two. Cover with broth, and add salt and pepper. Cook for about 30 minutes, until soft. (Add additional broth or hot water if the liquid evaporates, depending on your taste.)
Meanwhile, bring a large pot of salted water to a boil. Cook the pasta until al dente, drain it, and add to the lentils. Mix well together. Serve immediately with a sprinkle of Parmigiano.