Submerge mushroom in hot water until softened. Take them out, dry and finely juliene. Reserve water.
Heat some oil in a skillet, put in onions and let it sweat for a while. Stir in the rest of filling except boiled eggs and BBQ pork. Season with fish sauce and pepper to taste.
Add sugar to milk to dissolve. Add flour one cup at a time, after each time kneed the dough before adding the next cup. Put dough into a large mixing bowl, put a damp cheese cloth over to prevent drying out.
Cut a handful of dough (size to your choice), roll out thin (use bread roller or the smaller dumpling roller). Add a spoonful of filling, 1 piece of egg, BBQ pork. Seal dough tight around filling and put on a cut-out piece of parchment paper. Steam buns for about 15 minutes. These buns freeze pretty well as well, if you want to make a big batch at a time.