In a large mixing bowl, add glutinous rice flour, cornstarch, sugar, milk, coconut milk. Mix well and add melted butter.
Mix until everything is dissolved completely. (It’s important to make sure the mixture is smooth without any lumps.)
Transfer the mixture to a smaller bowl that can fit into your steamer.
Add a steaming rack to a large pot and add about 2 inches of water. Once boiling, place the bowl with the mixture into the pot.
Cover and steam for 10 minutes until the dough becomes slightly translucent. (To test the doneness, poke the dough using a spatula or fork, if there’s no liquid in the middle, the dough is ready.)
Transfer the mochi dough to another plate, cover with plastic wrap, and let it cool to room temperature. (Use oven mitts or kitchen towel when removing the plate from the steamer as it’s very hot!)
In the meantime, cut the mango into small square cubes (about 1/2 inch).
Wet your hands with water and take about 1 ½ tablespoon of dough. Form the dough into a ball and flatten it into a circular shape using your hands.
Place a piece of mango in the center. Pinch the four corners of the dough, and then pinch the remaining corners together.
Coat the mochi ball with shredded coconut. Chill the mango mochi balls in the refrigerator for at least 30 minutes before serving.