In a medium saucepan, combine the heavy cream, whole milk, granulated sugar, and salt. Heat over medium heat, stirring occasionally, until the mixture is hot and sugar is dissolved but not boiling, about 5-7 minutes.
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 egg yolk mixture back into the saucepan with the remaining cream mixture.
Cook over medium-low heat, stirring constantly with a wooden spoon or heatproof spatula, until the mixture thickens enough to coat the back of the spoon, about 5-8 minutes. Do not boil.
Remove from heat and whisk in the peanut butter and vanilla extract until smooth and fully combined.
Pour the custard through a fine-mesh sieve into a clean bowl to remove any cooked egg bits.
Cover the bowl with plastic wrap, pressing it directly onto the surface of the custard to prevent a skin from forming. Refrigerate until completely chilled, at least 4 hours or overnight.
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, about 20-25 minutes.
During the last 5 minutes of churning, add the chopped peanut butter cookies and allow them to incorporate evenly.
Transfer the ice cream to a freezer-safe container and freeze for at least 2 hours to firm up before serving.