In a large saucepan or Dutch oven, heat olive oil and cook onion until tender.
Add garlic and cook for 2-3 more minutes.
Add sweet potatoes, vegetable broth, bay leaves, and dried thyme.
Cook over medium heat until sweet potatoes are soft, about 20 minutes.
Stir in chopped kale and season with salt and pepper. Let simmer for 10 minutes. Serve warm.