In a large pot, heat 1/2 cup oil over mediumheat. Add onion, carrot, and celery. Sprinkle with salt and pepper to taste. Cook, stirring often, for 10 to 15 minutes or until the vegetables begin to soften and darken around the edges.

Add potatoes; sprinkle with salt and pepper. Cook, stirring occasionally, for 5 to 10 minutes or until the vegetables are nicely brown. Add 6 cups water, stirring to scrape up any brown bits from the bottom of the pot. Add tomatoes, bring to a boil, and then lower the heat to a simmer. Cook, stirring occasionally, for about 15 minutes.

Add zucchini and the kale, raising heat if necessary to keep the mixture at a steady bubble. Cook until the vegetables are very tender, another 10 to 15 minutes. Stir in the beans. Cook for 3 to 4 minutes. Add salt and pepper, if needed. Top with Parmesan cheese and a drizzle of olive oil.