01 - Combine heavy cream and whole milk in a medium saucepan. Heat over medium heat until just steaming, ensuring the mixture does not reach a boil.
02 - Whisk together egg yolks, granulated sugar, and salt in a separate bowl until the mixture appears pale and achieves slightly thickened consistency.
03 - Gradually pour approximately 1 cup of the hot cream mixture into the egg yolks while whisking continuously. This tempering process prevents the eggs from scrambling.
04 - Return the tempered egg mixture to the saucepan with the remaining hot cream, stirring to incorporate fully.
05 - Cook over low heat, stirring constantly with a wooden spoon, until the custard thickens enough to coat the back of the spoon (170-175°F). This process typically takes 5-7 minutes.
06 - Remove from heat and stir in peppermint extract, vanilla extract, and food coloring if desired, until fully incorporated.
07 - Pour the custard through a fine mesh sieve into a clean bowl. Allow to reach room temperature, then cover and refrigerate for at least 4 hours until completely chilled.
08 - Transfer the chilled custard to an ice cream maker and churn according to the manufacturer's instructions until it reaches soft-serve consistency.
09 - During the final 2 minutes of churning, add the finely chopped chocolate to allow even distribution throughout the ice cream.
10 - Transfer the churned ice cream to a freezer-safe container with a lid. Freeze for at least 2 hours until firm before serving.