Special Equipment: Ice Cream Maker Pastry bag with a straight medium tip (optional) Bakers' parchment
To make the ice cream, pour the milk into a heavy-bottomed pot. Bring the milk gently to a boil over medium heat, being careful not to scorch it or allow it to boil over. Lower the heat and simmer 10 minutes, uncovered. Remove from heat.
Meanwhile, in the large bowl of an electric mixer, bet the egg yolks and sugar together at medium speed 5 minutes. Then add several tablespoons of the hot milk to the egg/sugar mixture to temper the eggs. Return the pot of milk to the stove and, over low heat, add the egg yolk/sugar mixture in a slow, steady stream, stirring with a wooden spoon. Continue to cook 7 or 8 minutes, stirring constantly, until the custard has thickened and coats the back of a spoon. Remove from heat and cool completely in an ice water bath. Stir in the bourbon, rum, and nutmeg. When the custard has cooled completely, add the heavy cream and freeze according to the directions for your ice cream maker. While the ice cream is freezing, begin the pate a choux, the classic French pastry from which cream puff shells (profiteroles) are made.
Being careful not to break the yolks, break the eggs into a measuring cup or another container from which they can be poured one at a time, and set the container beside the stove. In a heavy-bottomed pot, bring the water, butter, salt, and sugar to a boil. When the liquid boils, stir in the flour all at once, using a wooden spoon. Reduce the heat to low and stir continuously 3 to 4 minutes, until the mixture pulls together and away from the sides of the pot. Chefs call this "cooking the flour out". What you are doing is coking away the raw flour flavor.
Still over low heat, add the eggs, one at a time, incorporating each egg individually until it is completely absorbed by the flour before adding the next one. During this process, the mixture will take on a shiny gloss and become very elastic. When all of the eggs have been incorporated, remove from heat, place the mixture in a stainless-steel bowl and cool completely.
To make the profiteroles, preheat the oven to 425 degrees. Using a pastry bag with a straight medium tip, pipe out approximately 1 rounded tablespoon batter for each profiterole onto a cookie sheet lined with lightly buttered bakers parchment, spacing them approximately 1 inch apart. If a bag and tip are unavailable, use a tablespoon to mound the batter on the bakers paper.
Brush each profiterole lightly with the egg wash, place in the preheated oven and bake 15 minutes before reducing the temperature to 350 degrees. Bake until the puffs are golden brown, about 12 minutes more. Remove from oven and allow to cool. When they have cooled completely, cut open and fill with a small scoop of ice cream. As you fill each profiterole, place it in the freezer to keep the ice cream frozen until you are ready to serve. To serve, place 1 profiterole on each plate, top with Fudge Sauce, and serve immediately.