Cookies:

1. Preheat oven to 350-degrees. Line your cookie sheet(s) with parchment paper or a silpat liner.
2. In the bowl of a stand mixer combine butter, oil, both sugars, and whipping cream (or milk), and cream together. Add eggs, vanilla, salt, baking soda and cream of tarter. Mix until combined (about 1 minute).
3. With mixer on low, add in flour and mix until combined. Add in the crushed candy cane and mix on low just until candy cane is evenly mixed in.
4. Roll the dough into golf ball-size balls and place them 2 inches apart on a cookie sheet. Dip the bottom of a glass (about 2 1/2 inches wide) in some granulated sugar and then gently press down on one of the cookie dough balls until about 1/2” thick.
5. Bake the cookies for 8-10 minutes, or until the bottom is lightly browned (don’t overbake these!). Let them cool for 5 minutes on the cookie sheet then move them to a wire rack to cool completely.
6. Frost with buttercream once they’re completely cooled.

Frosting:

1. In a large mixing bowl, mix butter until smooth and creamy, about 2 minutes.
2. With the mixer on low, slowly add in the powdered sugar. Once incorporated, add the oil/extract and the cream/milk and increase the speed. Mix until smooth and creamy, adding as much cream (or half & half)  as needed to get the consistency you want.  Continue mixing until frosting is smooth and creamy, scraping the sides of the bowl as necessary.