Beat eggs and sugar well with a hand whisk. Put beaten eggs and pandan leaves in a saucepan over a very gentle heat to dissolve the sugar.
When sugar has dissolved, remove the pan away from the heat and stir in thick coconut milk, mix well, then strain the mixture into a double boiler pot.
Cook over rapidly boiling water. Keep stirring the mixture with a long wooden spoon until it thickens; top up the boiling water in the lower pot whenever necessary.
Then wrap the lid with a big enough tea-towel (to prevent water dripping into the custard), replace it on the pot and steam the custard for two to three hours. (Do not stir the custard during this time.)
When kaya is ready, discard the pandan leaves.