Beat the sugar together with the egg yolks until well combined.
Pour the cream and milk into a saucepan and heat over a high heat until the mixture begins to foam and almost bubble over. Immediately remove the pan from the heat at this stage and pour the mixture over the eggs and sugar, being sure to beat vigorously the whole time so you don't end up with scrambled eggs.
Pour the mixture back into the saucepan and set the heat to medium. Stir the mixture constantly until it's thick enough to coat the back of a wooden spoon - this should take around 20 minutes.
When it's ready, remove the pan from the heat and pour in the vanilla and peppermint extracts. Stir, taste and add more of either extract if necessary.
Add in a couple of drops of green food colouring and stir. Add some more until you get the colour you're looking for.
Leave to cool to room temperature before pouring into an air-tight container and leaving in the fridge for at least 12 hours to cool.
When cool - if you're making the ice cream by hand - stir in the chocolate chips and place the container in the freezer. Remove the freezer every hour for six/eight hours and give the mixture a good stir before popping it back into the freezer.
When cool - if you're using an ice cream machine - pour the mixture into the machine and leave it to churn.
When it's done, scoop the ice cream into a separate container, stir in the chocolate chips and store in the freezer.