• Trim the root ends from the leek; cut the leek in half lengthwise, then crosswise into ¼-inch-thick half-moons. Soak the half-moons in a medium bowl of cold water, stirring occasionally to loosen any dirt, and allow the dirt to settle at the bottom. Skim the leek from the surface of the water and pat dry.
• Trim the ends from the celery; cut the celery into ½-inch pieces.
• Scrub or peel the potato; cut the potato in half lengthwise. Cut each half lengthwise into ½-inch-thick slices, the slices crosswise into ½-inch pieces.
• Rinse the white beans.
• Trim the stem ends from the green beans; cut the beans into 1-inch lengths.

• Coarsely chop the prosciutto.

In a large sauce pot over medium heat, warm 2 to 3 teaspoons oil until hot but not smoking. Add the prosciutto and cook, stirring occasionally, until lightly browned and beginning to crisp, 3 to 4 minutes. Remove the pot from the heat and spoon off the fat; keep the prosciutto in the pot.

To the pot with the prosciutto, add 2 to 3 teaspoons [1 to 2 TBL] oil. Warm over medium-high heat until hot but not smoking. Add the leek, celery, and potato and cook, stirring occasionally, until starting to soften, 3 to 5 minutes. Add the white beans, vegetable broth, and 2 cups [4 cups] water and bring to a boil. Reduce to a simmer, scrape up any browned bits from the bottom of the pot, and cook until all the vegetables are tender, 5 to 7 minutes. Add the green beans and cook until crisp-tender, 2 to 3 minutes. Remove from the heat and season to taste with salt and pepper.
When the soup is almost done, prepare the scallions.

• Trim the root ends from the scallions; thinly slice the scallions.

Transfer the soup to individual bowls, garnish with the scallions, and serve.