In a large bowl, combine rum, water and lemon juice. Add peeled apples and let marinade for one hour. In a separate bowl, combine crumbled Shortbreads, cinnamon, nutmeg and brown sugar. Pull apples from marinade and dredge lightly with flour. Take each apple, roll it in the egg wash, then roll and coat it completely in the cookie mixture.
Place apples in shallow glass dish and cover with foil.
Place in a 350-degree, preheated oven for 20 minutes. While apples are baking, bring frozen ice cream to room temperature. When apples are done and cooled, add room-temperature ice cream to pastry bag, and pipe into center of apples. In a saut pan, combine cream, sugar and vanilla extract and bring to a boil. Remove from heat, and whip cream and egg yolks into mixture.