Pre-heat the oven to 350 degrees F (180 degrees C).
Peel the carrots and slice them into thin rounds. Melt 3 tablespoons of butter in a medium pan.
Add the sliced carrots, chopped shallot, coconut milk, whole milk and cinnamon. Add salt and pepper.
Cover the pan and simmer the mixture for 20-25 minutes until the carrots are very soft.
Add half of the cilantro, roughly chopped, the last 5 minutes of cooking.
Allow the carrot mixture to cool for about 15 minutes.
Grease six (6) individual ramekins with the remaining 1/2 tablespoon of butter.
Pour the carrot mixture into a blender. Add the eggs and blend thoroughly. Carefully pour the mixture into the individual ramekins.
Prepare a bain marie. Place the ramekins in a large oven proof casserole and add boiling water to come up halfway on the ramekins. Bake for 30 minutes.
Garnish the ramekins with the remaining cilantro sprigs and serve while hot.