Process the basil, garlic, Parmesan, and olive oil in a food processor until smooth, about 15 seconds, scraping down the bowl as needed. The pistou can be refrigerated for up to 4 hours if making ahead.

Heat the olive oil in a Dutch oven over medium heat until it shimmers. Add the leek, celery, carrot, and salt; cook until the vegetables are softened and translucent, 8 to 10 minutes.

Stir in the garlic and cook until fragrant. Pour in the broth and water, then bring the liquid to a simmer.

Stir in the pasta and simmer until it begins to soften, about 5 minutes.

Add the haricots verts and simmer until they turn bright green but still maintain a slight crunch, about 3 minutes.

Stir in the cannellini beans, zucchini, and tomato. Simmer until the pasta is al dente and the vegetables are completely tender, about 3 more minutes.

Season with salt and pepper to taste and serve hot, topping each portion with a generous tablespoon of the pistou.