Place the butter, white sugar, and brown sugar with an electric mixer. Mix well until smooth. Add the eggs, vanilla, and peppermint extract to the butter mixture and mix well until combined.
In a second mixing bowl combine flour, cocoa powder, baking powder, and salt and mix until well blended.
Add the dry to the wet ingredients and mix until a thick sticky chocolate dough forms. Place the dough in the refrigerator and chill for 30 minutes.
Preheat the oven to 350 degrees. Line baking sheets with parchment paper.
Place the heavy whipping cream in a heatproof bowl. Place the chocolate chips and vanilla in a large bowl. Put the heavy whipping cream in the microwave and heat for 1 minute.
Pour the whipping cream over the chocolate chips. With a whisk, blend the chocolate chips with the whipping cream until smooth. Set the chocolate to the side.
Unwrap the candy canes or peppermint candies and place them in a thick ziplock bag. With a rolling pin, crush the candy canes in the bag until they are the size of large sprinkles.
Place the remaining sugar into a small bowl. With a medium cookie scoop, scoop and roll the cookie dough into balls. Roll each cookie dough ball in the sugar then place on a cookie sheet leaving two to three inches in between dough balls. With a teaspoon press the round part into each cookie dough ball.
Bake cookies for 10 to 12 minutes. When the cookies have just come out of the oven, push the teaspoon again into the center of each cookie to make the space to hold the ganache a little larger. Let the cookies cool completely on a wire rack.
Slide a large piece of parchment paper under the wire rack. With a small measuring cup carefully pour the chocolate ganache to fill the center of each cookie.
Sprinkle the tops of the cookies with crushed candy canes. Allow the ganache to fully set, then enjoy!