Make the filling: toast the Black Sesame Seeds in a dry skillet over medium heat until fragrant and slightly darker, then cool. Grind the seeds to a fine powder in a food processor or mortar, stir in Caster Sugar to taste, a small pinch of Salt, and work in Lard a little at a time until you have a thick, spreadable paste. Roll the paste into small chilled balls (about 1 teaspoon each) and refrigerate so they firm up.
Prepare the dough: place the Glutinous Rice Flour in a bowl and slowly add warm Water while mixing until a smooth, soft and pliable dough forms (it should not be sticky). Knead briefly, cover with a damp towel and let it rest for 10 minutes to relax.
Assemble the tangyuan: divide the dough into equal portions, flatten each into a small disc, place a chilled ball of black sesame filling in the center, then carefully pinch the dough closed and roll between your palms into a smooth ball so the filling is sealed inside.
Cook the tangyuan: bring a large pot of water to a gentle boil, add the dumplings and stir gently to prevent sticking. Once the tangyuan float, continue simmering for 2–3 minutes to ensure they are cooked through, then remove with a slotted spoon.
Make the ginger syrup: in a separate saucepan combine Water with thinly sliced Ginger and Rock Sugar; bring to a simmer and cook until the sugar dissolves and the broth is fragrant and slightly syrupy. Taste and adjust sweetness if needed.
Serve: place cooked tangyuan into bowls and ladle the hot ginger syrup over them. Serve immediately while warm—enjoy the chewy dumplings with the sweet, gingery broth.
