To make pandan juice, blend or pulverize pandan leaves with water in a food processor or blender, until as fine as possible. Strain the mixture, pressing it with the back of a metal spoon, to obtain pandan juice. Measure out 40 ml (leftover juice will keep well in an airtight container for up to 5 days, refrigerated).
In a mixing bowl, combine eggs and sugar, and whisk by hand until sugar dissolves, about 2 minutes. Add coconut milk and pandan juice, and stir to mix well. Strain the egg-coconut milk mixture into a small pot, that can sit inside a bigger pot.
Set up a double boiler or bain marie. Place the small pot inside the bigger pot. Carefully pour water into the bigger pot, until the water comes up the sides of the small pot (do not allow the water to overflow into the small pot).
Bring the water in the bigger pot to a gentle boil or simmer over medium fire, stirring the mixture continuously. As the mixture cooks, it will thicken and become sticky. Keep stirring until kaya is at the desired consistency. Pour out the kaya, and set aside to cool completely.
If a smooth, lump-free texture is desired, pour the cooked kaya into a food processor or blender, and pulse the mixture for a few seconds, or until desired smoothness. Set aside to cool completely. Once cool, store in an air-tight container and refrigerate.