Heat the vegetable oil in a large saucepan over medium heat. Stir in the onion and garlic; cook and stir until the onion has softened and turned translucent, about 5 minutes. Stir in the carrots and butternut squash; cook and stir until squash begins to brown, about 15 minutes.
Pour in the stock. Stir in the red potatoes, thyme, salt and pepper and bring to the boil. Reduce heat and simmer until vegetables are tender, about 45 minutes. Stir in the kale and cannellini beans and simmer until the kale is tender, about 10 minutes.
Pour about 750ml of the soup into a liquidiser, filling the jug no more than halfway full (you may have to do this in two batches). Hold down the lid of the liquidiser with a folded tea towel and carefully start the liquidiser, using a few quick pulse to get the soup moving before leaving it on to puree. Return the pureed portion of the soup to the soup pot, leaving the remaining soup chunky. Alternately, you can use a hand blender and partially puree the soup right in the cooking pot.