Put the stone in a large sauce pan. Add water to cover it by 3 inches. Boil for 1 minute. Add the beans, celery, parsley, tomatoes, splash of olive oil, garlic and carrot. Cook on a low heat for 30 minutes. Put a ladleful of soup in a blender and whiz for 10 seconds. Pour back into the pot. Add the salt and pepper. Cook for 10 minutes more. Boil up the tiny pasta in lots of salted water. When it's cooked (not too soft), drain it and add to the soup. If it looks too thick, add a bit of pasta cooking water so it's soupy. Put the basil in blender. Whiz for 10 seconds with 1/4 cup of olive oil and a teaspoon of salt. To serve: Ladle the soup into warm bowls and dribble on some basil oil and a sprinkle of grated Parmesan cheese.