Whisk the egg yolks and 1/2 cup of the sugar in a medium bowl until the mixture is pale and thick.
In a saucepan, combine the cream, milk, remaining sugar, salt, and ground coffee over medium heat.
Heat the dairy mixture until it begins to steam and small bubbles form around the edges, but do not let it reach a full rolling boil.
Slowly pour about half of the hot dairy into the egg yolk mixture while whisking constantly to temper the eggs.
Return the tempered egg mixture to the saucepan and cook over low heat, stirring constantly with a spatula, until the custard thickens enough to coat the back of a spoon, about 5 to 7 minutes.
Remove from heat and strain the custard through a fine-mesh strainer to remove the coffee grounds, then stir in the vanilla extract.
Cover the custard surface directly with plastic wrap and refrigerate until completely chilled, preferably for at least 4 hours.
Pour the chilled custard into your ice cream maker and process according to the manufacturer’s instructions until it reaches the consistency of soft-serve.
Fold in the chopped chocolate sandwich cookies by hand during the final minute of churning.
Transfer the mixture to an airtight container and freeze for at least 3 hours before serving to allow the texture to firm up.