2 Cream the butter and sugar together until very light. Add the eggs one at a time, beating after each addition, until very light. Add the lemon zest and continue beat another 3 minutes.
Whisk together the flour and baking powder and stir into the batter using the dough hook of an electric mixture. Add the applesauce and beat in thoroughly. Adjust the consistency of the batter with some milk. The dough should fall from a spoon in heavy sheets.
Pour batter into the prepared cake pan and smooth into an even layer. Score the top of the batter with a fork to prevent it from cracking as it bakes. Bake on a rack positioned in the middle of the oven for 60 to 70 minutes or until a toothpick inserted near the center of the cake comes out clean.
Let the cake cool in the pan for a few minutes, then unmold onto a wire rack and cool completely.
To serve, sprinkle with powdered sugar and cut into slices.