First, rinse the mung beans thoroughly, and soak them for 4 hours before cooking. Cook the soaked mung beans in a pot for about 20-30 minutes.
When the mung beans are cooked, and the water has almost evaporated, mix them with coconut milk, sugar, salt, and minced shallots.
Stir the mixture over low heat until you achieve a dry and smooth filling.
Allow the mung beans to cool, divide them into equal portions, and shape them into balls.
Divide the glutinous rice flour, warm water, and rice flour into 3 portions to make 3 different colored doughs for the rice dumplings. Place about 0.3 pounds of glutinous rice flour in a large bowl. Slowly pour in 4 tablespoons of warm water. Use a spatula to mix well. Next, gradually add pandan leaf juice/beetroot juice or room-temperature water (for the white dough). Knead the dough with your hands until it becomes fairly smooth, then add 1 teaspoon of rice flour. Continue kneading so that the dough is soft and pliable without being too dry, feeling wet but not sticky to the touch.Cover the dough with plastic wrap. Rest it for 30 minutes. Before shaping the glutinous rice balls, prepare a pot of boiling water so that you can cook them as soon as they are shaped. Divide the dough into equal portions. Shape each portion into a ball, flatten it with your hands, and place a mung bean ball in the center. Carefully wrap the dough around the filling, making sure not to expose the filling.
Gently roll the glutinous rice ball between your palms to form a round shape, then carefully drop it into the boiling water. Repeat this process until all the filling is used.
With the remaining dough, you can shape it into small, filling-free balls. While cooking the rice dumplings, gently stir them with a spatula to prevent them from sticking together. Use the spatula to gently push them so they don't stick to the bottom of the pot. Gently use a sieve to stir them, preventing them from sticking together. Cook over low heat until the dumplings rise to the surface (about 20 minutes). Remove them and place them into a bowl of cold water. Boil 1.2 quarts of water and add pandan leaves, cooking for about 5 minutes.
Add the rock sugar, stirring until it completely dissolves, before adding sliced ginger. Once you see the water come to a rolling boil, add the rice dumplings. Maintain low heat for about 10 minutes before turning off the stove. Pour coconut milk into a pot. Heat it over low heat until it simmers and thickens, then turn off the stove.
Scoop the rice dumplings into a bowl, along with some ginger syrup and sliced ginger. Drizzle with a bit of coconut sauce, and sprinkle some crushed peanuts, toasted sesame seeds, and julienned ginger on top.
Savor chè trôi nước with a spoon!