Preheat oven to 180°C. Grease a 20cm (base measurement) fluted tart tin with removable base.
Use an electric mixer to beat the sugar and egg yolks in a bowl until thick and creamy. Use a clean electric mixer to whisk the egg whites in a clean, dry bowl until soft peaks form. Fold the egg white and coconut into the yolk mixture until combined.
Spread the coconut mixture over the base and side of tart tin. Bake for 15 mins or until golden brown. Set aside to cool.
To make the custard filling, whisk the sugar, cream, coconut milk and eggs in a large bowl. Set aside until any bubbles subside. Pour the custard filling into the tart case in the tin. Bake for 35 mins or until just set. Set aside to cool to room temperature. Place in the fridge for 2 hours to chill.
Meanwhile, place the vanilla, extra sugar and plum in a medium saucepan over medium heat and cook, stirring, until sugar is dissolved. Bring to the boil. Cook for 5 mins or until plum has softened slightly.
Transfer the tart to a serving plate. Top with the plum mixture. Serve with whipped cream.