In a medium bowl, mix the chocolate and cocoa powder and set aside.
In a medium, heavy saucepan, heat the half-and-half over medium-high heat until almost boiling (bubbles will form around the edges).
In a heatproof bowl, whisk together the sugar and eggs until thick and pale yellow, about 2 minutes. Slowly whisk half of the hot half-and-half into the egg mixture and then pour the mixture into the saucepan. Bring just to a boil over medium heat and cook, whisking constantly, until bubbly and thickened, 1 minute.
Pour the custard through a sieve into the reserved chocolate-cocoa mixture and whisk until smooth. Let cool slightly, then press plastic wrap onto the surface to cover; refrigerate until cold, about 2 hours.
Scoop the chocolate pudding into individual cups and top with the whipped cream and cookies.