Preheat the oven to 375°F/190°C. Line a baking pan with parchment paper.
To make the donuts
In a medium bowl, beat the egg. Mix in the milk and peanut butter and beat until smooth. Using a fork, mix in the whole wheat flour and baking powder. On a flat surface, knead together until everything is well combined.
Roll out or pat the dough on a flat surface until it is about ½ inch (1 ¼ cm) thick. Using a small round cookie cutter, cut the dough into as many circles as you can fit. Using a smaller circular cutter (I used the large end of a frosting tip), cut out smaller circles in the middle of each circle to create the donut. Set the cut donuts on the pan. Roll the scraps of dough together and repeat this step, until you have used up as much dough as you can.
Bake for 20 minutes, until the donuts are dried and hard. Allow the donuts to cool.
To make the icing
In a small bowl, add in the carob powder and the boiling water. Mix until a smooth paste forms. If the icing is too stiff, add in water ½ teaspoon at a time.
Add the carob icing into a small icing squeeze bottle. Once the donuts have cooled, pipe the carob icing on top of the donuts. To keep the icing from cooling and hardening in the bottle, place it in a bowl of warm water when you are between donuts.
Notes
The carob icing does not stick well to the donuts and may flake off as you handle the donuts (ie. bag them up).