Preheat oven to 400º F.
Wash and peel the carrots, then cut them into pieces approximately 1" x .5".
Add the carrots and oil to a bowl and toss until the carrots are evenly coated. Place the carrots on a sheet pan line with parchment paper and bake in the oven for 15 minutes.
Remove the pan from the oven. Add 2 teaspoons of fresh dill to the carrots and return the pan to the oven. Bake for another 15 minutes, or until the carrots are soft.
Add the carrots, remaining 2 teaspoons of fresh dill, coconut milk and water to a blender. Puree until smooth, adding liquid until your desired consistency is reached.