For the crumb base: Throw the cookies and melted butter into a food processor and pulverize. Spoon some into the bottom of the serving glasses and set aside.
For the pudding: Combine the sugar, cornstarch and salt in a medium saucepan. Stir or whisk together. Pour in the milk and egg yolks and whisk together. Add the vanilla. Stir over medium heat until the mixture just barely comes to a boil and becomes thick, 6 to 8 minutes (maybe less, maybe more; just watch it!). The second it starts to bubble and thicken (note: it should be thick like pudding!), remove it from the heat. Add the white chocolate and butter and stir until everything is beautifully combined.
Pour the pudding into the glasses on top of the crumb base. Serve warm or chill in the fridge for 2 hours. Decorate with grated semisweet chocolate.