In a medium saucepan, combine heavy cream and whole milk over medium-low heat. Stir gently until the mixture reaches a temperature of 165°F.

In a heatproof bowl, whisk together egg yolks until smooth. Gradually add in granulated sugar, whisking until pale and fluffy.

Slowly drizzle the hot cream mixture into the egg yolks while whisking continuously. Return the mixture to saucepan and stir over low heat until thickened.

Strain the custard into a clean bowl set over ice to cool quickly. Refrigerate for at least 4 hours or overnight.

Stir in vanilla extract, peppermint extract, and salt. Add food coloring if desired.

Pour cooled custard into ice cream maker and churn according to instructions, about 20 minutes.

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

Transfer the churned ice cream into an airtight container and freeze for at least 2 hours.