Place glutinous rice flour, tapioca flour and shortening in a mixing bowl. Pour in water and mix into a soft and pliable dough. Pinch out dough into equal portions and roll into round balls of tong yuen.
Bring a pot of water to a boil, drop in the balls of tong yuen and cook until they start to float. Remove with a slotted spoon into a basin of cold water.
In the meantime, combine water, honey dates, white fungus, red dates and rock sugar and bring to a boil. Simmer for at least 20 minutes.
Add apricots and screwpine leaves. Simmer for another 2-3 minutes.
Dish out the white fungus soup and serve topped with the balls of tong yuen.