Peel and dice onions, celery, carrots and garlic.
Heat large soup pot or Dutch oven over medium heat. Add 2 tbsp olive oil. Add onions, celery, carrots and 1 tsp salt. Cook, stirring occasionally, for 6-8 minutes or until onions are soft and translucent.
Meanwhile, remove casings from sausages. When vegetables are soft add sausage and garlic. Using a wooden spoon, break up the sausage into small pieces and cook for 8-10 minutes or until sausage is cooked and starting to brown.
Add chicken stock and Parmesan rind if using. Increase heat and bring to a boil. Reduce heat and simmer gently for 15 minutes.
Meanwhile, rinse and drain beans. Place 1/3 to 1/2 of the beans on a plate or cutting board and mash with a fork. After soup has simmered for 15 minutes add the whole and mashed beans and continue simmering for another 15 minutes.
Add arugula and chopped basil. Simmer 5 more minutes. Add more stock if you want to thin it out more. Remove from heat and add fresh lemon juice. Taste and adjust seasonings, adding more salt and/or pepper as needed.
Garnish each serving with some freshly grated Parmesan cheese. Serve with crusty bread or make Parmesan crostini by thinly slicing a baguette, sprinkle with Parmesan and broil on a tray until browned.