01 - Combine heavy cream and milk in a medium saucepan. Heat over medium heat until just steaming, being careful not to bring to a boil.
02 - Whisk egg yolks, sugar, and salt in a separate bowl until mixture becomes pale yellow and slightly thickened in texture.
03 - Gradually pour approximately 1 cup of the hot cream into the egg yolks while whisking continuously. This prevents the eggs from scrambling.
04 - Pour the tempered yolk mixture back into the saucepan with the remaining cream, stirring to incorporate fully.
05 - Cook over low heat, stirring constantly with a wooden spoon, until the custard thickens and coats the back of the spoon (170-175°F). This takes approximately 5-7 minutes.
06 - Remove from heat immediately. Stir in peppermint extract, vanilla extract, and food coloring if using until evenly distributed.
07 - Pour 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 thoroughly chilled.
08 - Process the chilled custard in an ice cream maker according to the manufacturer's instructions until it reaches a soft-serve consistency.
09 - Add the finely chopped chocolate during the final 2 minutes of churning to ensure even distribution throughout the ice cream.
10 - Transfer the churned ice cream to a freezer-safe container with a tight-fitting lid. Freeze for at least 2 hours until firm before serving.