Follow your ice cream machine manufacture's instructions for best results (normally in the user manual also likely available online). Use the Built-in Compressor feature to make ice cream immediately or place the ice cream bowl in the freezer for at least 24 hours prior to use.
In a pan/pot: add sugar, whole milk, heavy whipping cream, peppermint extract, green food color and whisk. Cook on low-medium for 5 minutes or until sugar is dissolved. Stir frequently as it may burn or scorch. Turn off the heat source.
In a small bowl: whisk the egg yolks. Add 2 tbsp of the milk mixture into the yolks and whisk. Repeat this step 2 more times. Whisk the milk mixture and slowly pour the yolk mixture into the pan while whisking. Turn on the heat source and cook on low for 8 minutes (stir frequently).
Place a mesh/strainer on top of a bowl. Pour the mixture through the strainer. Cover with saran wrap - place a piece of saran wrap directly over the surface of the mixture (this will prevent skin forming). Refrigerate/chill for at least 6 hours or overnight.
The next day- chop the chocolate bar into small chucks and tiny pieces.
Then turn on the machine and make sure the ice cream maker is properly churning. Slowly pour the cream mixture into the stainless steel/freezer bowl and churn for 60 min. The last 5 minutes add the chocolate into the ice cream and continue to churn until done.
Once ready, serve immediately or transfer the ice cream to an air tight container with lid. Place in the freezer for at least 6 hours to form the proper ice cream texture.