Beat together the sugar and eggs in a bowl until pale and thickened. Set aside.
In a medium saucepan, bring milk to a simmer. Slowly drizzle the hot milk into the sugar mixture, whisking the whole time. Pour the mixture back into the saucepan. Stir constantly with a whisk until the custard thickens slightly and coats the back of a spoon. Do not let the mixture boil or the eggs will scramble. Remove the saucepan from the heat and stir in the peanut butter. Place a large fine mesh strainer over a large bowl. Pour custard through the strainer to get rid of any lumps. Allow mixture to cool slightly then stir in the cream and vanilla. Cover tightly and refrigerate until cold or overnight.
Stir the cold custard then add to your ice cream machine. Churn according to manufacturers instructions. In the last five minutes, add the cookie crumbles. Remove ice cream to a bowl and carefully swirl the peanut butter throughout. Don't stir too much or you will lose the swirled effect. Eat right away or freeze in airtight container.