For the coating flour, in a medium nonstick pan over medium heat, without adding any oil, add 70 grams glutinous rice flour. Stir with a spatula constantly and toast until lightly golden brown, about 5 minutes. Transfer to a large plate to cool completely.
In a large pot or wok (with lid), put in the steaming rack and add water that reaches 1-inch below the top of the rack. Bring the water to a boil over medium heat.
For the dough, in a medium mixing bowl, whisk together glutinous rice flour, cornstarch and sugar. Add vegetable oil and water. Whisk until smooth.
For the mangoes, rinse under running water and pat dried. Cut the mangoes in 3 parts lengthwise. Remove the pit. Carefully scoop out the flesh in one piece with a large spoon. Pat dried with paper towels and set aside.
Pick a medium bowl or deep plate that can be steamed and fit in the wok. Lightly wipe the inside of the bowl with vegetable oil. Transfer the batter into the bowl.
Carefully place the bowl on top of the steaming rack. Cover the wok with a lid and steam for about 15 - 18 minutes. To see if the dough is cooked though, poke into the center with a chopstick or a fork. If you don’t see any white flour in the dough, it’s ready. If not, steam for a couple more minutes. Carefully remove the bowl and place on a pot holder. If you see water collected on top of the dough, pour that out.
In a large bowl, wipe the inside with a thin layer of vegetable oil. Lightly coat a stiff spatula or wooden spoon with vegetable oil as well. Transfer the dough into the bowl. While the dough is still hot, stir and fold it for about 4 minutes. This stretches the dough and gives it a more elastic texture. Cover with plastic wrap and set aside until just cool enough to handle. It should still be very warm.
For the wrapping, set up the working surface. First, if you have a food scale, cover it with plastic wrap. Then place a 10x15-inch piece of plastic wrap on your working surface. Make sure it sticks to the table well. If needed, put a little water underneath. Next, set the coating flour nearby. Last, prepare a large plate for the finished rice cakes.
Put on food safe plastic gloves. Take out about 80 grams of dough by measuring on the scale. It will be slightly bigger than a golf ball. Roll into a ball and place on the prepared plastic wrap on the table. Pat down slightly and stretch into an oval shape large enough to cover half a mango, focusing on patting down the edges thinner. Place half a mango with flat side facing up on the dough. Pull the center parts of both long sides of the dough to connect over the mango. Then wrap one end by pulling the dough up from the bottom. Once that side is wrapped, continue with the other side. By now, the mango should be fully covered with dough. It’s ok that the dough is not perfectly smooth because this side will be the bottom.
Carefully transfer the rice cake to the coating flour. Keep your gloves free of flour, as the dough will not be sticky if it gets covered with flour. Use a large spoon to cover the rice cake with flour and leave it there for now. Continue with the remaining rice cakes. Once all the rice cakes are done, use your gloved hands to roll and coat each one thoroughly in the flour. Dust off any excess and place the finished rice cakes on the clean prepared plate.
The rice cakes are ready to be served. If not serving right away, wrap with plastic wrap individually and store in an airtight container. If you like the rice cake with a softer texture, keep at room temperature. If you prefer a chewier and slightly firmer texture, keep in the fridge. Enjoy within 24 - 36 hours.