From the pineapple, trim the stalk and the crown of the leaves so that the flesh is visible. Stand the fruit upright and cut the skin from top to bottom. Now cut the pineapple in half lengthwise, separate out the hard inner core and cut the halves into bite-sized pieces.
Melt the butter, sprinkle in 2 tbsp of sugar and fry until frothy. Add the pineapple and cook over low heat for 5 minutes until soft. Extinguish with the rum. Remove from heat and simmer briefly in a closed saucepan. In the meantime, beat the yolks with the remaining sugar in a metal bowl in a hot water bath until light and fluffy. Add the coconut milk and warm it up. Next, cool the sauce in a cold water bath while continuing to beat. Whip the whipped cream until stiff and fold it in.
Arrange the still-warm pineapple pieces in small dessert bowls and spread the coconut milk evenly over them.