Preheat the oven to 350 degrees.
Lightly grease a small cake pan or ramekin.
Whisk the flour and baking powder together in a bowl.
In a separate bowl, mix the egg, applesauce, peanut butter, and water.
Combine the wet and dry ingredients.
Stir gently until the batter is smooth.
Pour the batter into the prepared pan.
Smooth the top lightly.
Bake for 18 to 22 minutes.
Check for doneness by inserting a toothpick; it should come out clean.
Remove the cake from the oven.
Allow the cake to cool completely before frosting or serving.