In a medium saucepan, combine the heavy cream and whole milk over medium-low heat. Stir occasionally and watch for bubbles forming at the edges.

In a separate heatproof bowl, whisk the egg yolks until smooth. Gradually add in granulated sugar while whisking continuously until thick and pale.

Carefully pour the hot cream mixture into the egg yolk and sugar bowl, whisking constantly to temper. Return to saucepan and cook over low heat until it reaches 165°F.

Strain the custard through a fine mesh sieve into a large bowl in an ice bath. Stir gently until cooled, about 10-15 minutes. Refrigerate for at least 4 hours.

Stir in vanilla extract, peppermint extract, salt, and optional food coloring to the cooled custard. Pour into ice cream maker and churn for about 20 minutes.

In the last 30 seconds of churning, add the crushed Oreo cookies gently.

Transfer the ice cream to an airtight container, removing air pockets. Freeze until solid, about 2 hours.