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Warm the oil in a large, heavy saucepan (that has a lid), stirring in the thyme.
Add the peas and turn them in the garlic-flavored oil, then tip in the prepared leeks, potato, celery, zucchini, and green beans and stir in the heat of the pan.
Pour in the water, add the salt, put the lid on the pan and let come to a boil, then—you will have to keep an eye, or certainly an ear, on it to tell when—remove the lid and let everything bubble cheerfully for 10–15 minutes or until the vegetables—check the potato particularly—are tender.
You could let the soup stand at this stage; if I’m planning to press forward within an hour or so, I put the lid on to keep in the heat; otherwise it is better to let it cool swiftly before reheating.
Remove 3 ladlefuls of soup mixture, trying to scoop up more vegetables and less liquid, and tip into a blender (or a large bowl if you’re using an immersion blender) and set this aside.
Add the drained, rinsed cannellini or flageolet beans to the pan and bring back to a boil, then add the tortelloni and bring it all up to a boil again. Turn off the heat.
Add the basil and Parmesan to the reserved vegetables in your blender or bowl and whizz to a vibrant green purée, then scrape this back into the pan, stirring it into the soup. Let it stand for 10–15 minutes before eating.