Mix together pork, barbecue sauce, shallots, flour, chicken stock, soy sauce, oil, and sugar. Chill in refrigerator for at least 6 hours.
Preheat grill for medium heat and lightly oil the grate. Cook the pork until an instant-read meat thermometer reaches 145 degrees F (63 degrees C). Allow to cool; shred or finely chop the meat.
Prepare dough for Chinese Steamed Buns (see footnote).
Shape dough into balls. Roll each out into a circle, (like won-ton wrappers). Put 1 tablespoonful of prepared meat mixture in the center of each circle, and wrap dough around filling. Place seam-side down onto wax paper squares. Let stand until doubled, about 30 minutes.
Bring water to a boil in wok, and reduce heat to medium; the water should still be boiling. Place steam-plate on a small wire rack in the middle of the wok. Transfer as many buns on wax paper as will comfortably fit onto steam-plate, leaving 1 to 2 inches between the buns. At least 2 inches space should be left between steam-plate and the wok. Cover wok with lid. Steam buns over boiling water for 15 to 20 minutes.
REMOVE LID BEFORE you turn off heat, or else water will drip back onto bun surface and produce yellowish "blisters" on bun surfaces. Continue steaming batches of buns until all are cooked.