Preheat the oven to 350°F (180°C). Grease a 9 x 13-inch baking dish with nonstick spray.
In a large bowl, whisk together the melted butter and sugar until combined. Add the eggs, and beat until fully incorporated. Add the vanilla, baking powder, and mochiko flour and whisk until fully combined. Add the evaporated milk and coconut milk and whisk until a smooth batter is formed.
Transfer the batter to the prepared baking dish and spread in an even layer, then bake for 45–50 minutes, until golden brown. Let the butter mochi cool to room temperature in the pan.
While the butter mochi cools, make the glaze: In a medium bowl, whisk together the powdered sugar and coconut milk until smooth and thick. Add more coconut milk, 1 tablespoon at a time, if needed.
Once the butter mochi has cooled, spread the glaze all over the top and sprinkle with the toasted shredded coconut. Slice into small squares and serve.