Preheat an oven to 350 degrees F (175 degrees C). Whisk the flour and baking powder together in a small bowl.
Beat the white sugar, oil, and egg together in a bowl until smooth. Stir in the flour mixture alternately with the milk. Pour into a 9-inch square pan. Dissolve the brown sugar in the hot water, then pour stir in the melted butter. Drizzle the syrup over the pudding.
Bake in the preheated oven until the pudding firms and becomes golden brown on top, about 40 minutes.