Clean the Tuscan kale well and remove the leaves from the stalks. You can see how to do this here.
Thinly slice the leeks and add them to a large pot with the ⅓ cup olive oil and salt. Cook over medium-low heat until tender, being careful not to burn them, about 10 minutes. A bit of gold color is fine but if you find the onions are browning quickly, turn the heat down.
Meanwhile, clean and peel the potatoes, if you like. If not, leave the skin on and chop them into a small dice, about ¼ inch wide.
Add the potatoes to the cooked leeks and cook for another 10 minutes or so.
Meanwhile, roughly chop the kale. Add it to the potatoes along with the broth of your choice and salt. If you are using water, you may need to add more salt. If you are using pre-prepared broth, reduce the salt to ½ teaspoon and taste for seasoning later on.
Let simmer, uncovered for 25 minutes. Add the apple cider vinegar and puree with an immersion blender. If you prefer to use a blender, allow the soup to cool down a bit before pureeing.
If you are adding the cream, add it right before serving. Serve with croutons or crusty bread.