Beat the egg yolks in a bowl until they turn a light lemon yellow color, about 3 or 4 minutes. Set aside.

Combine the whipping cream, milk and the remaining sugar in a heavy-bottom saucepan.

Cook over medium heat, whisking often, until the sugar has dissolved and the mixture is hot.

Ladle about 1 cup of the hot mixture into the beaten egg yolks, whisking constantly until well-blended and smooth.

Pour the egg yolk mixture into the saucepan and continue to cook over medium heat, whisking constantly, until the mixture thickens enough to form a film or coat the back of a spoon, about 5 minutes.

Remove from the heat and add peppermint extract.

Let the mixture cool to room temperature then freeze in an ice cream maker according to the manufacturer’s instructions.

After churning the ice cream for about 2 minutes add the crushed Oreos and peppermint pieces. Continue to churn until thick and ice cream consistency.

Freeze in airtight container for at least 1 hour before serving.

In a bowl beat together butter and sugar until light and fluffy.

Add egg and vanilla and beat until combined.

In a separate bowl, combine flour, baking soda and powder and salt, mix to combine.

Gradually add flour to butter/sugar and mix until just combined.

Add buttermilk or cream and mix again, until just combined.

Stir in candy cane pieces.

On a parchment lined baking sheet, roll out dough balls and space about 2 inches apart.

Bake at 375 for 10 minutes.

Scoop out ice cream and sandwich between two cookies. Roll in extra candy cane or crushed oreos. Eat immediately, or wrap individually and freeze.