Heat olive oil in a large pot over medium heat. Add onion and cook until softened, about 5 minutes. Add garlic, ginger, and red pepper flakes and cook for 1 minute more.
Add sweet potatoes and vegetable broth to the pot. Bring to a boil, then reduce heat and simmer for 20-25 minutes, or until sweet potatoes are tender.
Remove from heat and carefully blend the soup using an immersion blender or in a regular blender (in batches).
Stir in peanut butter and lime juice. Season with salt and pepper to taste.
Stir in kale and cook until wilted, about 2-3 minutes.