Cook pancetta in oil and butter in a large saucepan over a medium heat, 3 minutes. Stir in onions and cook until softened, about 7 minutes.
Add carrots, celery, garlic and ¼ tsp salt and cook, stirring occasionally and patiently, until browned, about 20 minutes. Push vegetables to one side and add tomato paste, stirring until it turns a couple of shades darker, about 2 minutes. Peel and thinly slice potato (those slender sections will give the soup an unctous underbelly) and stir in along with water, tomatoes with their juice, green beans, and cheese rind. (If you’re squeamish about the idea of overcooked beans, don’t be; meltingly tender green beans are delicious.)
Bring soup to a gentle simmer and cook, partially covered, 1 hour. Stir in cannellini, kale, and parsley and simmer, partially covered, 25 minutes longer. Season. Serve soup drizzled with olive oil and grated cheese if you like. If you want to add spoon-sized cooked pasta, stir it in right before the soup hits the table.