Outside chocolate cookie dough

1. In a large bowl or bowl from stand mixer, beat butter with sugar until light and fluffy.

2. Beat in egg and vanilla, mixing well to combine.

3. In a small mixing bowl, combine flour, baking powder salt and cocoa powder. Mix well until all the cocoa powder is incorporated into the mixture.

4. Gradually add flour/cocoa  mixture to butter mixture, mixing on low after each addition until well combined, then set aside.

Inside Peppermint Cookie Dough

5. In a medium-sized mixing bowl, beat butter with sugar until fluffy. 

6. Beat in milk and peppermint extract. 

7. Add in flour and salt and stir just until combined.

Assembling the cookies

8. Using 1 tbsp. each of the chocolate dough, roll into 2 balls. Flatten balls into 1/4" thick circles one at a time and set aside.

9. Next, using 1 tsp. of the white peppermint dough, roll into ball and place over one of the chocolate circles. 

9. Top with the second chocolate circle, pressing around the edges to seal.

10. Repeat with remaining dough.

11. Bake cookies, 2 inches apart on a parchment paper-lined baking sheets in a 350F oven for 15 minutes. 

12. Allow cookies to cool on baking sheets for 5 minutes, then transfer to cooling racks and cool completely.

Frosting

13. In a stand mixer fitted with paddle attachment, beat butter and powdered sugar. Add in half and half and beat for 1 minute. Mixture may need a bit more half and half. Add more to reach spreadable consistency 1 tsp. at a time.

14. Once cookies have cooled completely (approximately 20 minutes), frost the tops with icing. 

15. Top with crushed candy cane garnish.