Bring a large pot of salted water to a boil. Wash and chop the carrots (no need to peel), and add them to the boiling water. Bring the water back to a boil, then cover the pot and cook at medium heat until the carrots are soft (about ten minutes).
While the carrots cook, saute the diced apple in the coconut/olive oil until soft. Add the cinnamon and ginger to the apples and cook until fragrant.
Once the carrots are cooked, drain them. Add the apples and water/broth to the pot, and heat until everything is warm. Puree with an immersion blender, or add everything to a high-powered blender (such as a Vitamix) and blend until smooth.
Season with salt and pepper to taste. Serve with coconut yogurt or sour cream.