Italian Potato Soup

4 Large Potatoes, peeled and diced
1 Carrot, peeled and diced
2 Stalks of Celery, diced
1 Small Onion, diced
¼ cup of Tomato Puree
2 Tbsp of Olive Oil
Fresh Basil Leaves
Salt and Pepper
1 ½ cups Small Shaped Pasta
5 cups Water
Freshly grated Parmiggiano Reggiano