In a medium saucepan, whisk together the cocoa powder, sugar (3/4 cup plus 2 tablespoons), corn starch, and salt until well combined.
Gradually whisk in the whole milk, ensuring no lumps form. Place the saucepan over medium heat and continue whisking until the mixture begins to thicken and bubble gently, about 5-7 minutes.
In a separate bowl, whisk the egg yolks. Slowly ladle about a cup of the hot mixture into the egg yolks while whisking constantly to temper them.
Pour the tempered egg yolk mixture back into the saucepan with the remaining hot milk mixture. Cook over medium heat, stirring continuously until the pudding is thick and glossy, about 2-3 minutes more. Remove from heat.
In a heatproof bowl, add the chopped unsweetened chocolate. Pour the hot pudding mixture over the chocolate and let it sit for a minute to melt. Then whisk until the chocolate is fully incorporated, followed by the vanilla extract.
In a small skillet, combine the sugar (1/4 cup) and cocoa nibs. Cook over medium heat, stirring constantly until the sugar dissolves and coats the nibs, turning a golden brown. Spread on parchment paper to cool.
Pour the chocolate pudding into serving dishes and let it cool slightly. Top with the caramelized cocoa nibs before serving. Refrigerate for at least 2 hours before enjoying.