Mix together glutinous rice flour, cornstarch, sugar, milk, and coconut milk in a large bowl.

Add melted butter and mix until everything is dissolved.

Transfer the mixture to a smaller bowl that can fit into your steamer.

Add a steaming rack to a large pot over medium heat and add 2 inches of water.

Once boiling, place the bowl with the mixture into the pot.

Cover with a lid and steam for 10 minutes until the dough becomes slightly translucent.

Transfer the mochi dough to another plate, cover with plastic wrap, and let it cool to room temperature.

Cut the mango into half-inch square cubes.

Wet your hands with water and take about 1 ½ tablespoon of dough.

Shape the dough into a ball and flatten it 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.