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 medium-sized heatproof metal or glass mixing bowl.
Set up the double boiler. Fill a medium-sized deep pot with about two inches of water. Set the water-filled pot on your stove-top heating element. Bring water to a gentle, continuous simmer over low to medium heat. Set the heatproof mixing bowl containing the kaya mixture over the pot, making sure the base of the mixing bowl does not come into contact with the simmering water.
Stir the mixture frequently with a whisk as it gently cooks. As the mixture cooks, it will gradually thicken and become sticky. Keep stirring until kaya is at the desired consistency. This may take about 40 mins, depending on how your double-boiler is set up. When it thickens to a soft paste, pour out the kaya, and set aside to cool completely. Note: The kaya will firm up a little more as it cools.
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.