Using a large, heavy knife, “shave” the chocolate into fine shreds by slicing downward at an angle onto your cutting board. Set aside.
Whisk egg in a heavy medium bowl until yolk and white have completely combined.
In a medium saucepan off-heat, whisk brown sugar, cocoa powder, cornstarch and salt. Slowly dribble in milk, whisking all the while. (Mixture may have undissolved bumps.)
Set saucepan over medium heat, and bring to a boil. As pudding cooks, use a heatproof spatula to make figure eights along the pan’s bottom, sweeping the sides occasionally as you stir. Once you get a genuine boil, reduce the heat slightly to prevent scorching, but allow to bubble steadily for 2 minutes. Stir constantly with heatproof spatula.
Remove from heat, and spoon about 1/4 of mixture atop the beaten egg, whisking egg vigorously as you add the chocolate mixture. Scrape tempered egg mixture back into saucepan, set over low heat, and cook, stirring constantly, for another minute. (Be gentle with the heat as you don’t want scrambled eggs.)
Remove pudding from heat, and stir in vanilla and 3/4 of shaved chocolate. Divide among ramekins.
To serve, sprinkle with remaining shaved chocolate. Enjoy warm, at room temp or cold. (Cover and refrigerate, if waiting to enjoy later).