Preheat oven to 360°F (180°C) degrees. Grease a 9-inch springform pan with 1 tablespoon vegetable shortening.
Separate the yolks and egg whites into separate bowls.
Blanch, peel and toast the almonds on a baking sheet at 360°F for 5-10 minutes. Grind them in a food processor and set aside. To reduce the preparation time, buy peeled blanched almonds in the store and grind them.
Beat the butter, adding sugar and beating until mixture is smooth in a large bowl.
Add egg yolks one at a time, continuously mixing. Add the ground almonds and shaved chocolate and mix well on low with a hand mixer.
Pour in the milk and rum in another bowl. Soak the ladyfingers in the milk mixture until soft, then add to the butter-sugar mixture. Mix well. Add the flour and cornstarch and mix.
Beat the egg whites to a stiff point, which takes about 5 minutes with an electric hand mixer. Fold into the batter using a spatula.
Pour the mix evenly into a Muffin Top Baking Pan. If you do not have one you can use a cupcake pan.
Bake in the oven on middle rack for about 25 minutes. Check the cookies after 15 minutes. The cake is done when a toothpick is inserted into the center and comes out clean.
Cool the cake on a rack. When cool, remove the sides of the pan.
Place one cookie on a small plate. Place one scoop of ice cream on the cookie. Garnish with salted pistachios.