Remove outer leaves of leeks and discard. Trim off dark green leaves and freeze in plastic bag to save for future stock. Slice down the length of leeks and rinse well, opening each layer to reveal the inner parts. Slice thinly. Set aside.
Remove outer skins of shallots. Slice thinly. Set aside.
Peel garlic and mince. Set aside.
Wash and trim celery. Slice thinly. Set aside.
Wash, peel, and and quarter potatoes. Then cut into ¼” thick slices. Set aside.
If using rind, wash and scrap a thin layer from the outside. Set aside.
Heat olive oil in large soup pot. Add shallots and saute a few minutes. Add leeks and celery and stir for a few minutes. Add garlic and stir. Do not brown garlic. (Add hot pepper flakes if using.) Add potatoes.
Add enough water to completely submerge the vegetables by about 6cm. Bring to a boil and then reduce heat to simmer.
Add rind, if using. Season lightly with salt and pepper. Set lid to cover partially. Simmer for about 30 minutes, or until potatoes are tender.
While soup is simmering, prepare the other vegetables.
Trim escarole and place in bowl of cold water to rinse well. Strain and chop in large pieces. Set aside.
Wash and remove stem and scar from zucchini. Quarter and slice. Set aside.
Wash and chop the parsley. Set aside.
After 30 minutes of simmering the soup, add the parsley, escarole, and zucchini, and beans. Stir and simmer for about another 20 minutes, stirring occasionally. Add more water if needed.
Taste for seasonings. (Remove rind, if using. Can be finely chopped and added to soup.) Stir and serve immediately with freshly grated Parmigiano Reggiano and a drizzle of extra virgin olive oil.