Preheat the oven to 375 F. Set ramekins or baking dishes on a baking sheet
Put the applesauce and chocolate in a medium-sized bowl, and set the bowl over a pan of barely simmering water, stirring until smooth.
Using an electric mixer, whip the eggs, and sugar until mixture is light and foamy, and just holding its shape - about 5 minutes, longer by hand. Fold 1/3 of the beaten eggs into the chocolate, then scrape the lightened chocolate mixture over the beaten eggs, and fold it in just until there are no streaks of eggs visible.
Divide the batter into the baking dishes. Fill as much or as little as you want.
Bake the puddings on the lower rack of the oven for about 15-20 mins, until the puddings are puffed up, but a toothpick inserted into the centre comes out with some soft, "gooey" chocolate attached.