To a medium saucepan add the butter, coconut milk, water, and salt over medium heat. Allow all the butter to melt and bring the mixture to a boil. As soon as the mixture begins to boil, reduce heat to medium-low and add in the flour. Using a wooden spoon, mix thoroughly to incorporate the flour. Continue stirring until the dough starts to pull away from the sides and a thin film forms on the bottom of the pan (about three minutes). Remove the mixture from heat and transfer to a large mixing bowl. Let the dough cool slightly. Add in the eggs, one at a time, being sure to fully incorporate each egg before adding the next.