In a mixing bowl, whisk the eggs until light and fluffy (2-3 minutes). Add the sugar a little at a time, whisking along the way, until fully incorporated (at least 1 minute). Set aside.
In a medium sauce pan, heat the milk on medium until bubbles start forming around the perimeter of the pan.
Remove pan from heat and slowly add the heated milk to the sugar/egg mixture, whisking the whole time. Give it a good whisking for a minute and then return the whole thing to the sauce pan. Heat on medium, stirring frequently, until the custard coats the back of a wooden spoon with a film.
Remove from heat, transfer to a covered bowl, and chill in the refrigerator for at least 4 hours.
Remove the custard from the refrigerator and add to it the cream and Sailor Jerry spiced rum, mixing thoroughly.
Freeze in your ice cream machine according to manufacturer’s recommendations.
In a covered container, spread a layer of cookie crumbs, then ice cream, then a layer of cookie crumbs, then ice cream.
Chill in the freezer for 4 hours, or until it reaches desired consistency.