Preheat the oven to 160°C or 325°F. Grease a 20-centimeter round cake pan and line the base with parchment paper.
Whisk the egg yolks with half of the sugar until pale and creamy. Mix in the oil, coconut milk, lime juice, lime zest, pandan extract, and optional food coloring.
Sift in the flour and salt, then stir gently until smooth. Fold in the coconut flakes.
Beat the egg whites until foamy. Gradually add the remaining sugar and beat until glossy, firm peaks form.
Fold the whipped egg whites into the batter in three additions, using a spatula and taking care not to deflate the mixture.
Pour the batter into the prepared pan and bake for 50 to 60 minutes, or until a skewer inserted in the center comes out clean.
Cool the cake in the pan for 10 minutes, then transfer it to a wire rack and cool completely.
Whisk the powdered sugar with the fresh lime juice until thick and pourable. Drizzle the lime glaze over the cooled cake before slicing.