Preheat oven to 350°F. Line square 8-inch baking dish with parchment paper. Generously butter parchment paper. Set aside. *Alternatively, use a 9x13-inch glass baking dish for a thinner cake. No need for parchment. Generously butter dish and set aside.
Place butter and chocolate chips in a microwave safe bowl. Heat for 30 second intervals on 50% power until ingredients are melted and mixture is smooth. Stir often to ensure even melting. Set aside to cool slightly.
In a large bowl, whisk together sweet rice flour, sugar, cocoa powder, baking powder, and salt.
In a separate bowl, whisk together eggs, evaporated milk, and coconut milk. Pour liquid mixture into dry ingredients. Whisk or stir together until there are no longer any dry steaks of flour and mixture is smooth.
Pour in slightly cooled chocolate butter mixture. Stir until well distributed. Pour mixture into prepared baking pan. Bake in the center of oven for 50-55 minutes until toothpick inserted in center comes out clean.
Allow mochi butter cake to cool before unmolding.