Cheesy Bibingka Cake

Ingredients

• 1/4 cup softened unsalted butter
• 3/4 cup granulated sugar
• 3 large eggs, room temperature
• 3/4 cup rice flour (not glutinous)
• 3/4 cup all-purpose flour
• 1 tbsp baking powder
• 1/2 tsp salt
• 1 cup coconut milk
• 1/2 cup water
• 3/4 - 1 cup grated cheddar cheese plus more for topping
• 1 piece thinly sliced salted egg for topping