Preheat oven to 320 F. Grease and line a loaf or round cake pan with parchment paper.
Sift flour, baking powder, and salt into a bowl, then mix in shredded coconut.
In a separate bowl, whisk eggs and sugar until pale, then whisk in yogurt and coconut milk.
Gently fold dry ingredients into the wet mixture in two additions.
Fold in melted butter, followed by the floured lychees.
Transfer batter to prepared pan and smooth the surface.
Bake for 55–65 minutes, until the top springs back and a skewer comes out clean.
Cool in pan for 5 minutes, then transfer to a rack and cool completely.
Melt white chocolate gently over simmering water, then stir in oil.
Allow glaze to cool slightly, then pour over cooled cake.
Let glaze set fully before slicing and serving.