Melt butter in a large saucepan over medium heat. Add onion; cook 8 minutes or until tender, stirring frequently. Add garlic; cook 30 seconds, stirring constantly. Stir in broth, potato, salt, and bay leaf; bring to a boil. Cover, reduce heat, and simmer 15 minutes or until potato is tender.
Stir in kale and basil. Cover and simmer 10 minutes or until kale is tender. Discard bay leaf. Partially mash potatoes with a potato masher until thick and chunky. Top with cheese.