Preheat the oven to 180°C (350°F).
Separate the egg whites from the yolks. Beat the egg whites until stiff peaks form.
In a separate bowl, whisk the egg yolks with sugar and vanilla until pale and fluffy.
Gently fold the egg whites into the yolk mixture, followed by the sifted flour, baking powder, and shredded coconut.
Pour the batter into a lined baking tray and smooth the surface.
Bake for 12-15 minutes until golden and springy to touch.
Invert the cake onto a clean tea towel dusted with powdered sugar.
Roll the cake gently with the towel and let it cool completely.
While the cake cools, prepare the filling by whisking cream cheese, powdered sugar, and coconut milk until smooth.
Unroll the cooled cake carefully and spread the filling evenly over the surface.
Re-roll the cake without the towel and wrap in plastic wrap.
Chill the roulade for at least one hour before slicing.