Heat oil in a large saucepan. Sauté the onion and garlic for about 5 minutes. Add the water, potatoes, and salt and pepper, and cook for 20-25 minutes over medium heat, stirring occasionally.
Stir in the kale, beans, and parsley and cook for 5-10 minutes more. To thicken the soup, mash the potatoes against the side of the pan with a wooden spoon. Take off heat and let sit for about 10 minutes more.