Split the vanilla bean lengthwise and scrape the seeds into a saucepan. Add the vanilla pod, milk, cream, sugar, cinnamon stick and salt; bring to a simmer over medium heat. Remove from the heat, cover and steep 15 minutes.
Whisk the cornstarch and egg yolks in a large bowl. Slowly whisk in the warm milk mixture, then pour the mixture back into the saucepan. Bring to a boil over medium heat and cook, whisking constantly, until thick, about 3 minutes. Stir in the butter. Pour the pudding through a fine-mesh sieve into a bowl; let cool slightly.
Divide most of the cookie crumbs among small glasses. Top with the pudding. Cover with plastic wrap and refrigerate until cold, about 3 hours. Top with the remaining cookie crumbs.