Preheat your oven to 350°F.
In a large mixing bowl, whisk together the flour, sugar, baking powder, and salt. Make a well in the center of the dry ingredients and pour in the coconut milk, melted butter, and eggs. Whisk everything together until you have a smooth and creamy batter.
Generously grease a 9-inch cast-iron skillet with butter, lard, or vegetable shortening.
Pour the batter into the skillet. Place the pan in the oven and bake for 15 minutes.
Remove the cake from the oven and top it with slices of salted duck egg if using. Add the grated cheese to the top of the cake. Return the skillet to the oven and continue to bake until the bibingka is golden brown and a toothpick inserted into the center comes out clean, approximately 20 to 25 minutes.
Remove the baked cake from the oven and brush it with 2 tablespoons of melted butter.
Sprinkle the top with coconut flakes. Set aside to cool for about 15 minutes or longer.
Slice the cake into 6 wedges and serve with your holiday meal or with a nice cup of tea.