The complex flavor of this stew will have 'em thinking you've been simmering it for hours. Adding the kale leaves at the very end ensures they keep their structure.
Heat oil in a large pot over medium heat. Add onion, garlic, carrots, and celery and season with salt. Cook vegetables, stirring, until tender, about 8 minutes.
Increase heat to medium high and add tomatoes and their juice. Cook, stirring, until mixture begins to caramelize, about 3 minutes.
Add 7 cups water, potatoes, and beans, and bring soup to a boil. Reduce heat and simmer until potatoes are tender, about 10 minutes, then stir in kale.
Cook, covered, until tender, about 2 minutes, then season with salt and pepper. Top with Parmesan.
Toss a Parmesan rind into the broth while cooking. It will heighten the richness of the soup.