Process the basil, Parmesan, oil, and garlic in a food processor until smooth, about 30 seconds; set the pistou aside.

Heat the oil in a large pot over medium heat until it shimmers. Add the leek, celery, carrot, and a pinch of salt and pepper; cook until the vegetables are softened and the leeks are translucent, about 5 to 7 minutes.

Stir in the garlic and cook until fragrant, about 30 seconds.

Stir in the vegetable broth and water. Increase the heat to high and bring the liquid to a boil. Add the orecchiette and cook until it is just beginning to soften, about 8 minutes.

Stir in the haricots verts and white beans. Continue to simmer until the beans are slightly tender, about 3 minutes.

Add the zucchini and tomato. Simmer until the zucchini is tender and the pasta is al dente, about 2 minutes more.

Remove the pot from the heat and season with salt and pepper to taste. Serve hot, with a generous dollop of the pistou swirled into each bowl.