Bring a pot of water to boil.
Place the coconut oil in a medium heat safe bowl.
Place the bowl of coconut oil in a large baking dish and safely pour the hot water into the baking dish, around the water. (This is called heating "bain marie"). Heat until the coconut oil is melted to 98-99F (use a candy thermometer)
Place a second large bowl over a bed of crushed ice.
In the bowl over the ice, add the sunflower oil and whisk.
Add the mustard powder and salt, keep whisking.
Add the carrot juice, keep whisking.
Slowly add the coconut in the coconut oil. Keep on whisking until it becomes firm to your liking.
Place over seran wrap or parchment paper and form into a log about 2 inches thick. Wrap and store in the fridge until ready to slice and serve!
Vegan butter properly stored will last in the fridge up to 14 days.