To prepare filling: Combine black sesame paste, sugar, butter, salt and water in a small bowl. Mix until it holds together. Take a tiny portion and press well together to form a very tiny ball. Leave aside the balls of filling.
Place glutinous rice flour, tapioca flour and green tea powder in a mixing bowl. Add shortening and make a well in the centre. Gradually add water and mix into a soft and pliable dough.
Divide dough into equal portions and set aside covered with a piece of clingfilm.
Take a portion of green tea dough and make a small dent in the centre. Add a ball of black sesame seeds filling. Wrap up neatly and roll into a round ball of tong yuen.
Bring a pot of water to the boil. Drop the balls of tong yuen into the water and bring to a boil. When the dough balls float, remove them with a slotted spoon.
Put them into a basin of cold water. Allow to steep in the cold water while preparing the tea soup.
For the tea soup: Boil water and sugar in a small saucepot.
Once the sugar dissolves drop in the sachets of green tea. Allow to steep for two minutes.
Discard the tea bags and drop the balls of cooked tong yuen into the syrup.
To serve, dish out tong yuen into individual bowls and serve immediately.