Place 10 small jars of 4 to 5 ounces or demitasse cups on a sheet pan and set aside.
In a large saucepan, bring the half-and-half to a simmer.
In the bowl of a stand mixer fitted with the whisk attachment or in a large bowl, whisk together the egg yolks, brown sugar, cornstarch, vanilla, and salt until very smooth. Slowly and carefully, pour the hot half-and-half into the yolk mixture, pouring the half-and-half down the side of the bowl and making sure to whisk constantly.
Once everything is combined and smooth, return the mixture to the saucepan and whisk constantly over medium heat until the mixture thickens to the consistency of thick mayonnaise, making sure not to allow the mixture to boil vigorously.
Immediately fill each prepared jar/demitasse cup about half to three-quarters full. Add the chocolate to the remaining budino/pudding in the saucepan and stir until melted. Divide the chocolate budino among the small jars and then cover each with a small amount of plastic wrap, making sure the plastic wrap touches the exposed pudding so a skin doesn’t form. Refrigerate until cool and set, about ½ hour to 1 hour.
Whisk together the heavy cream or whipping cream and the confectioner’s sugar until you achieve medium/stiff peaks. Top the cooled puddings with the whipped topping and serve.