Heat the oven to 400°F and grease a 9-by-13-inch baking dish.
Melt the butter in a large saucepan and cook the onion over medium heat until soft, 6 minutes.
Stir in the flour and cook for 1 minute, then gradually whisk in the warm broth and milk.
Simmer until thick enough to coat a spoon, 4 to 5 minutes, and stir in the Worcestershire, salt and black pepper.
Fold in the pulled pork, frozen vegetables and barbecue sauce and cook until the mixture just begins to bubble.
Spread the hot filling in the baking dish and arrange the separated biscuits over it with a little space between them.
Bake until the filling bubbles and the biscuits are deeply browned and cooked through, 25 to 30 minutes.
Rest the pot pie for 10 minutes before serving.