Preheat oven to 350 degrees F (175 degrees C). Grease an 8-inch square baking dish.
In a small bowl combine the dates and baking soda. Pour enough boiling water over the dates to just cover them.
Cream 1/3 cup of butter with the white sugar until light. Beat in the eggs and mix well to combine.
Add the flour and date mixture (including water) to the egg mixture and fold to combine. Pour the batter into the prepared baking dish.
Bake in the preheated oven until a tester comes out clean, 30 to 40 minutes. Let cool slightly and prepare the sauce.
To Make Caramel Sauce: In a small saucepan combine the brown sugar, 1/3 cup butter, and evaporated milk. Cook over medium heat and bring to a boil. Turn the heat down and simmer for 5 minutes, stirring occasionally. Remove from heat and stir in the vanilla. Pour the sauce over individual servings of warm cake. Yields one pudding.