In a medium saucepan, combine the heavy cream, whole milk, granulated sugar, and salt. Heat over medium heat until the mixture is hot and sugar is dissolved, but do not let it boil.
In a separate bowl, whisk the egg yolks until smooth.
Slowly pour about 1 cup of the hot cream mixture into the egg yolks while whisking constantly to temper the eggs.
Pour the tempered egg yolk mixture back into the saucepan with the remaining cream mixture.
Cook over medium-low heat, stirring constantly with a wooden spoon or spatula, until the mixture thickens enough to coat the back of the spoon (about 170°F or 77°C). Do not boil.
Remove the saucepan from heat and stir in the vanilla extract.
Pour the custard through a fine mesh sieve into a clean bowl to remove any cooked egg bits.
Let the custard cool to room temperature, then cover and refrigerate for at least 4 hours or overnight until thoroughly chilled.
Once chilled, pour the custard into an ice cream maker and churn according to the manufacturer’s instructions until it reaches a soft-serve consistency.
Fold the chopped oatmeal cookies gently into the churned ice cream.
Transfer the ice cream to an airtight container and freeze for at least 2 hours to firm up before serving.