Dairy Queen Candy Cane Chill Blizzard

2 cups vanilla ice cream, divided
2 tablespoons milk
2 candy canes, broken into smaller pieces
1/4 cup chocolate chunks

Place 1 cup of ice cream in a blender with the milk and broken up candy canes.
Pulse until the candy canes and milk are incorporated.
Remove the mixture from the blender and add the additional cup of ice cream and the chocolate chunks.
Using the back of a spoon mix the vanilla ice cream into the mixture until it is fully incorporated.
Add more milk or ice cream to achieve the desired consistency.