Preheat the oven to 350 degrees F.
In a dry pan over medium heat, toast the black sesame seeds until they start popping and fragrant, stirring periodically. Remove from both the heat and hot pan once toasted (be careful not to burn).
In a food processor, grind the toasted black sesame seeds. Be careful to not overgrind or the oils will make it chunky. Just enough that the seeds are ground down (about 15-30 seconds).
In a standing mixer or large bowl, add the mochiko, sugar, baking powder, toasted sesame seed powder, and combine.
Add the eggs, milk, coconut milk, softened butter, and vanilla extract. Mix well.
Oil or butter a 9 x 13 inch baking pan. Then pour the batter into the pan and flatten out so it's even.
Bake for 50-60 minutes. Set aside to cool down completely.
Cut the butter mochi into squares and enjoy! Store at room temperature.