Preheat your oven to 350 degrees F and lightly coat six 8-ounce glass jars with non-stick cooking spray.
Whisk together the flour, 1/4 cup cocoa powder, granulated sugar, baking powder, and salt in a medium bowl.
Stir in the milk and applesauce until the batter is smooth, then divide the mixture evenly among the prepared jars.
In a small bowl, combine the brown sugar, the remaining 1/4 cup cocoa powder, and the chocolate chips, then sprinkle this mixture evenly over the batter in each jar.
Heat the half and half in the microwave until it is steaming hot but not boiling, then stir in the vanilla extract.
Carefully pour the hot liquid over the top of the dry topping in each jar without stirring the contents.
Arrange the jars on a baking sheet so they are not touching and bake for 30 minutes until the tops are set and the sauce is bubbling.
Remove from the oven and let the jars rest for 5 minutes before serving to allow the pudding layer to thicken slightly.