1) In a large mixing bowl blend together the cream and milk. Add the eggs and sugar, whisking until the mixture begins to thicken.
2) Add the vanilla pudding mix or pastry cream filling mix and whisk until dissolved.
3) Stir in the peppermint oil and crushed candy canes, and continue to stir for about 1 minute. This will allow the smallest pieces of candy to dissolve and begin to turn the mixture pink.
4) If you want the ice cream to be brighter pink, add a few drops of food coloring.
5) Chill the ice cream base for 2 hours minimum, or up to overnight. A cold base will freeze faster, resulting in a smoother ice cream.
6) Freeze the base in your ice cream maker according to the manufacturer's directions. If desired, add extra crushed peppermints or more candy cane bits to the mix during the last 5 minutes of freezing.