In a mixing bowl, beat cream cheese with granulated white sugar, peppermint extract, and vanilla extract until fluffy and smooth. Portion out the mixture onto a lined tray and freeze for about 30 minutes, until firm.

In a separate bowl, whisk together all-purpose flour, baking soda, baking powder, and salt. In another bowl, cream together butter, light brown sugar, and granulated white sugar until light and fluffy.

Incorporate egg yolks, peppermint extract, and vanilla extract into the butter-sugar mixture. Gradually add the dry ingredients, blending thoroughly. Fold in white chocolate chips and crushed candy cane pieces.

Preheat your oven to 350°F. Take about 2 tablespoons of cookie dough and flatten it. Place a frozen cheesecake ball in the center, encase it with dough, and roll into a ball.

Roll the cookie ball in granulated sugar and place on a baking sheet, leaving space between each. Bake for 10-12 minutes, until edges are golden and centers are soft.

Allow cookies to cool on the baking sheet for 5 minutes before transferring to a wire rack. Sprinkle with extra crushed candy cane pieces before serving.