Preheat the oven to 350°F with a 10-inch cast-iron skillet in it.
In a large bowl, using a wooden spoon, stir together the mochiko flour, baking powder, sugar, matcha powder, and salt. In a medium bowl, whisk together the eggs, coconut milk, evaporated milk, vanilla, and melted butter. Pour the wet ingredients into the dry, stirring with a wooden spoon until you have a green batter. Make sure all the dry ingredients at the bottom of the bowl have been completely integrated (Don’t worry about overmixing this batter.) Fold in the bananas.
Pour the batter into the pan and bake for 1 hour, until the top of the cake is golden and just browned around the edges. Enjoy warm, out of the pan, or at room temperature. The cake is best stored at room temperature, wrapped in plastic wrap or in a sealed container for up to 3 days. Zap it in the microwave for that warm, just-baked effect.