Freeze the mints, while you prepared the ice cream mixture.
Beat the egg yolks in a large mixing bowl until light yellow and set aside.
In a 3 quart saucepan over low heat, melt the butter, and then add the sugar, and stir until combined. Add the milk, and bring to just a simmer. Remove from heat and add half to the eggs. stirring, to temper the eggs, and keep them from curdling. Then add the egg mixture back to the pot, and cook on low, stirring, until the custard coats the back of your spoon , about 8 minutes.
Pour the mixture through a strainer into a clean bowl. Stir in the cream and vanilla and put it into the refrigerator until cold, for at least an hour, but preferably overnight.
Put the mixture in your ice cream maker and churn. Add the mints, according to your ice cream maker's instructions.
Serve right away for a softer texture, or freeze overnight for a harder ice cream.