Preheat the oven to 350°F (180°C) and lightly grease a 9x13 inch (23x33 cm) pan, or line it with parchment paper, leaving some overhang for easy removal. In a large bowl, cream the butter, cream cheese, and granulated sugar until the mixture is smooth and no lumps remain. Incorporate the egg, additional yolk, and peppermint extract, blending thoroughly. Sift together the flour, baking powder, and salt, then gradually mix into the creamed base on low speed, stopping once fully integrated. Distribute the dough evenly into the prepared pan and press it flat. Bake for 22–25 minutes, or until the top appears set and the edges show the slightest golden hue.

For the frosting, begin by beating the butter until creamy. Blend in 2 cups of powdered sugar, half a teaspoon of peppermint extract, and the salt, starting on a low speed. Continue adding the remaining sugar half a cup at a time, alternating with a tablespoon of cream, until the desired consistency is reached. Optionally, mix in additional peppermint extract and red food coloring for a festive touch. If parchment was used, lift the cooled bars from the pan using the overhang and place them on a cutting surface. Otherwise, leave the bars in the pan. Smooth the frosting over the completely cooled cookie base using a flat-edged knife and finish with crushed candy canes. Cut cleanly with a sharp, thin blade and remove using a metal spatula.