Place red mung beans in a food processor and pulse until it becomes smooth and paste-like. If too dry, add more of the reserved syrup. Set aside.
Combine all ingredients for the dough in bowl except for the water. Gradually add water while mixing the dry mix from time to time until a dough forms. Just use enough water. The dough should not be too wet and soft but also not dry and crumbly. It should be easy to handle and form.
Turn the dough into a ball and lightly flatten it a bit. Using a knife or bench scraper, divide the dough into 16 equal parts, like you would a pizza.
Take a piece of the dough and roll it into a cylinder about 3 inches long. Flatten it with using your fingers (or use a rolling pin) about half centimeter thick.
Scoop about a tablespoon of red mung bean paste and spread it in the middle of the flattened dough. Now fold the sides towards the middle to enclose the filling inside. Do the same with the rest of dough.
Fill a large pot with water and bring to a rolling boil. Gently drop some of the filled doughs one by one into the boiling water. Do it in 2 or 3 batches. Just make sure they are not over-crowded. Once they float remove them from the pot using a slotted spoon.
Transfer them to a baking dish arranged in a single layer. Bake at 200°C until tops turns brown.
Combine rice flour and sugar in a small pot or saucepan. Gradually add some coconut cream to the dry ingredients while mixing just to moisten it and prevent it from forming lumps. Mix until smooth. Add the rest of coconut cream and bring the mixture into a simmer over low heat until it turns into a thick sauce. Turn off the heat and add the vanilla extract and mix.
Pour some of the sauce over the moche, reserve some for toppings later. Return to oven and bake for another 10 minutes
Alternatively, you can also fry the mochi in coconut oil until the sides are brown.