Whisk the pudding and 2 cups milk together in a bowl until thickened, about 2 minutes. Refrigerate the pudding until serving time.
Mix blueberries and 1/2 cup sugar in a large saucepan and pour in enough water to just barely cover the berries. Bring the mixture to a boil over medium heat, reduce heat to low, and simmer while you make the dumplings.
To make dumplings, mix flour, baking powder, 1 tablespoon of sugar and salt together in a bowl. Make a well in the center of the flour mixture and pour in vegetable oil and 1 cup of milk. Stir until the mixture forms a soft dough.
Bring the berry mixture back to a boil, and drop the dumpling dough into the boiling blueberries by heaping spoonfuls. Cover and simmer over medium-low heat until the dumplings are cooked through, about 15 minutes. A knife inserted into a dumpling should come out clean. To serve, scoop a dumpling into a serving bowl, spoon blueberry sauce over and top with chilled vanilla pudding.