Preheat the oven to 375°F. Grease a nonstick mini loaf pan or muffin pan thoroughly, including the corners and up the sides.
In a large bowl, whisk together the mochiko, sugar, baking powder, and salt until no lumps remain.
In a separate bowl, whisk the coconut milk, water, melted butter, eggs, and vanilla until smooth.
Pour the wet ingredients into the dry and whisk until the batter is smooth and pourable, with no streaks of dry flour.
Divide the batter between the prepared pans, filling each well nearly to the top. The mochi rises only slightly, so it won't overflow.
Bake for 40 to 45 minutes, until the surface and edges are deep golden brown and the center feels set when lightly pressed. In a 9x9 baking dish, bake for about 1 hour.
Remove the pieces from the pan and set them on a wire rack. Cool completely, 2 to 3 hours, before serving. This is what firms them up into the chewy texture, so don't cut them warm.