When the pork is done cooking remove the meat with a slotted spoon to a large bowl, fishing out and discarding the star anise pods. Mash the meat with a potato masher (a dinner fork would work also), leaving it on the chunky side. Skim the fat that has floated to the top of the liquid in the pot with a small ladle and discard. Crank the heat to high and reduce the liquid until you end up with about 1 cup, 7-8 minutes. Add enough of the liquid to make the meat saucy without being soupy. You may not use all the liquid. Set aside to cool.
When the dough has doubled in size, deposit it onto a floured countertop and knead for 3 minutes, adding small amounts of flour as needed to prevent sticking. Form the dough into a ball and divide in half. Roll one of the halves into a 6-inch log shape and cut into 6 equal pieces (46-47 grams each-a digital scale is helpful here.) Repeat with the other half of the dough. Cover the balls with a clean kitchen towel and rest 15 minutes.
Lightly grease a half-sheet pan with a little of the oil and have standing nearby. Roll out one of the balls with a rolling pin or small dowel to a circle 5-inches in diameter. Place a couple tablespoons of the pork mixture in the center of the circle then fold the edges up and over the filling. Pinch the pleats with your fingers then give it a little twist to seal, being mindful to remove as much air from the buns as possible. Place seam-side down on the prepared sheet pan. Repeat with the remaining dough balls, placing them 1/2-inch apart from each other. You should be able to fit all 12 balls. Cover with a clean kitchen towel and rest 30 minutes.
Crank your oven to 375℉ and place a rack in the middle position. Brush the buns with the egg wash and poke a few holes in the tops with a toothpick to allow steam to vent. Bake for 20 minutes.
Remove the buns from the oven and cool for 15 minutes before consuming.