Preheat your oven to 375°F (190°C) and prepare a round cake pan or baking dish by lining it with pre-cut banana leaves. Lightly heat the leaves over an open flame or stove burner for a few seconds to make them pliable and release their natural aroma before placing them in the pan.
In a large mixing bowl, combine the rice flour, baking powder, and salt. Whisk together until evenly blended, then set aside. In a separate bowl, cream the butter until soft and smooth. Gradually add the sugar while whisking continuously until the mixture becomes light and fluffy.
Crack in the eggs, one at a time, whisking well after each addition to fully incorporate. Slowly fold in the dry mixture of rice flour, salt, and baking powder, stirring gently until just combined.
Pour in the coconut milk and fresh milk alternately while whisking to form a smooth, thick batter. Continue mixing for another 1 to 2 minutes to ensure the ingredients are fully integrated.
Pour the prepared batter into the banana leaf-lined pan, spreading it evenly. Place the pan in the preheated oven and bake for 15 minutes, or until the surface begins to set. Remove the pan from the oven, and while still hot, arrange the slices of salted duck egg on top, followed by a generous sprinkle of grated cheese.
Return the pan to the oven and bake for an additional 15 to 20 minutes, or until the top turns a beautiful golden brown and a toothpick inserted into the center comes out clean. Once baked, take the bibingka out of the oven and allow it to cool slightly.
Brush the surface with melted butter for a glossy finish and top with freshly grated coconut before serving. Enjoy this soft, aromatic Filipino rice cake warm — perfect with a cup of coffee or hot chocolate.