Heat the oil over medium heat in a pot or Dutch oven. Sauté onion until it begins to turn translucent, about 8 to 10 minutes.
Add the sweet potato and continue cooking until sweet potato is soft, stirring frequently.
Add the artichoke hearts, chicken broth, cayenne, nutmeg and salt and bring to a boil.
Reduce heat and simmer 10 minutes.
Add the kale leaves and cover the pot until kale leaves have wilted, about 1 minute.
Pour the soup into a blender with the almond milk and blend until smooth. This will likely need to be done in batches.
Strain the soup into the same pot you used for cooking in order to catch the strands of artichoke hearts.
If serving the soup hot, pour it back into a pot and heat gently, stirring frequently until the soup is to desired temperature. If serving chilled, pour the soup into a sealable container and refrigerate until cold.
Serve with crusty bread and a drizzle of oil on top.