In a large pot or Dutch oven, melt butter over medium heat.
Add onion, carrots, and celery and cook until softened, about 5-7 minutes.
Add garlic and cook for another minute until fragrant.
Pour in chicken broth and bring to a boil.
Add wild rice and reduce heat to a simmer. Cover and cook for 20-25 minutes, or until rice is tender.
Stir in sweet potato and cook for another 10 minutes, or until tender.
Add kale and coconut milk and cook until kale is wilted, about 5 minutes.
Season with salt, pepper, and paprika to taste.
Serve hot.