Preheat the oven to 350°F (175°C).
Grease or line a 9x5x3 inch loaf pan.
Cream the butter and brown sugar in an electric mixer.
Add the egg, vanilla and applesauce and beat until light and fluffy (about one minute).
Sift the flour, baking powder, baking soda, salt and cinnamon together into a large bowl.
Add the dates and walnuts to the flour mixture, stirring to coat. (This prevents the dates from sticking together.)
Remove the bowl from the electric mixer and thoroughly stir the flour, date and nut mixture into the creamed applesauce mixture using a wooden spoon.
Transfer the batter to the prepared pan and bake for 60 to 70 minutes. Keep an eye on the cake towards the end of baking to make sure it doesn't get too brown.You can cover the cake loosely with a bit of aluminum foil at this point to prevent over-browning if necessary. The cake is done when a skewer inserted in the centre of the cake comes out clean.
Remove from the oven and cool in the pan for 20 minutes before turning out on to a wire rack to cool completely.