Put the onion, celery and carrots into a large saucepan with the oil and once the vegetables are sizzling, add the water or the stock. Cook gently, stirring often, until the vegetables are soft. Add the garlic, tomato purxe9e and the balsamic vinegar, and cook on a high heat for a minute more.
Then add the diced vegetables, lentils, and tomatoes and bring to boil. Reduce the heat and simmer for about 40 minutes, adding a little water or stock if necessary.
Bring a large saucepan of slated water to boil. Put the pasta into the water and stir thoroughly. Replace the lid and return to the boil. Remove or adjust the lid once the water is boiling again. Cook according to the packet instructions until al dente.
Drain the pasta and return it to the pot. Season the vegetable ragu and pour over the pasta, mixing well. Serve immediately, sprinkled with Parmesan cheese.