This is an Italian dessert that originated in Piedmont (in northwest Italy) that was traditionally served at noble banquets dating back to the 13th century. It's a rich, soft dessert similar to pudding or custard. Many versions of this recipe can be found based on regional variations, but this version is from Langhe area of Piedmont, which is a hilly area of Italy that is famous for its wines, cheeses, and truffles.
In a medium bowl, beat the egg yolks with the sugar until smooth.
In a food processor, combine the egg yolk mixture with the crushed amaretti, cocoa, milk and rum. Process for a couple of minutes until very well mixed. Strain the mixture into a bowl. Gently fold in the egg whites.
Pour into four 2-inch individual molds or a single large 10-inch ring-mold.
Set the mold(s) in a roasting pan and add hot water to reach halfway up the sides of the molds. Bake in the oven at 300° for about 30 minutes, or until set. Let cool completely.