In a large bowl, blend together the flour, sugar and baking powder.
Add blueberries and toss to distribute them in the flour mixture.
Add the melted butter, milk, and vanilla extract.
Using a wood spoon, mix all together until a soft dough is formed.
Place dough in a wet heavy cotton pudding bag.
Tie the bag tightly, to avoid water passing through, with a piece of butcher string.
In a large pot, boil gently for approximately 1-½ hours to 2 hours; add additional water, if necessary.
Remove from pot, remove pudding from bag, place on a chopping board and slice.
Place on individual serving plates, top with blueberry or rum sauce.