Christmas Cookie Ice Cream

In a medium saucepan over medium heat, combine the heavy cream, whole milk, half of the sugar, and the salt. Heat the mixture, stirring occasionally, until it is steaming hot but not boiling, which should take about 5 minutes.
In a separate medium bowl, vigorously whisk the egg yolks with the remaining sugar until the mixture becomes pale yellow and slightly thickened, about 2 minutes.
Slowly pour about 1 cup of the hot cream mixture into the egg yolk mixture while whisking constantly to temper the eggs. Then, gradually pour the entire egg mixture back into the saucepan while stirring.
Cook the custard over medium-low heat, stirring constantly with a wooden spoon, until it thickens enough to coat the back of the spoon and reaches 170°F on an instant-read thermometer, about 5 to 7 minutes. Do not let it boil.
Immediately strain the custard through a fine-mesh sieve into a clean bowl. Stir in the vanilla extract. Cover the bowl and refrigerate until completely chilled, at least 4 hours or overnight.
Pour the chilled custard into your ice cream maker and churn according to the manufacturer's instructions until it reaches a soft-serve consistency, about 20 to 25 minutes.
Gently fold in the crumbled Christmas cookies and optional peppermint bark with a spatula until evenly distributed throughout the ice cream.
Transfer the ice cream to an airtight container, press a piece of parchment paper directly onto the surface, and freeze until firm, at least 4 hours or overnight.