Sauté the Leeks: Heat olive oil or coconut oil in a large soup pot or Dutch oven over medium heat. Add the sliced leeks and sauté until softened, about 5 minutes.
Add the Veggies and Spices: Toss in the carrots, apples, vegetable stock, apple cider, turmeric, cinnamon, ginger, and a pinch of salt and pepper. Stir everything together and bring the mixture to a simmer.
Cook Until Tender: Let the soup simmer for about 30 minutes, or until the carrots are tender.
Blend: Once the carrots are soft, use an immersion blender (also known as a hand blender) to purée the soup until smooth. If you prefer a thinner consistency, feel free to add more stock, water, or cider. You can also use a food processor or standard high speed blender to purée.
Finish with Coconut Milk: Stir in the coconut milk and honey. Taste and adjust seasoning if needed. If you want a sweeter soup, add a touch more honey.
Serve: Ladle the soup into bowls and, for an elegant touch, swirl in additional coconut milk and drizzle with honey. A sprinkle of freshly ground black pepper or a cinnamon stick makes a great garnish! Serve with a bit of bread for a heartier meal.