Preheat the oven to 350°F (180°C) and grease a 9x9-inch baking dish.
In a microwave-safe bowl, melt the butter, then add the coconut milk and mix until combined.
In a separate bowl, whisk together the eggs, sugar, and vanilla extract.
Gradually add the egg mixture to the butter mixture, stirring until well combined.
In a large bowl, whisk together the mochiko and baking powder.
Slowly add the mochiko mixture to the wet ingredients, stirring until the batter is smooth.
Pour the batter into the greased baking dish and smooth the surface.
Bake for 1 hour, or until the top is golden brown and a toothpick inserted into the center comes out clean.
Allow the mochi to cool completely before cutting it into squares.
Serve and enjoy!