Preheat the oven to 300 degrees F.

In a large bowl, combine room temperature butter, ½ cup powdered sugar, and vanilla extract. Beat on medium speed until smooth.

In a medium bowl, whisk together flour and baking powder. With the mixer on low speed, gradually add the dry ingredients to the butter mixture. Turn the mixer to medium speed until the mixture is just blended.

Place high-quality bittersweet chocolate chips in a metal bowl set over a bowl of simmering water, stirring until the chips are melted. Let the melted chips cool for 4 to 5 minutes and then add to the butter mixture. Beat on medium speed until blended. Stir in candy cane pieces.

Using a scant 1 tablespoon of dough for each cookie, shape the dough into balls and place on baking sheets lined with parchment paper, about 1 inch apart.

Bake the cookies until they are pale golden brown, 25 to 30 minutes, switching the position of the pans halfway through baking. Let the cookies stand on baking sheets for about 30 minutes. Place 1½ cups powdered sugar in a medium bowl. Working with a few cookies at a time, roll the cookies in the powdered sugar until coated. Lightly brush off an clumps of powdered sugar that may form.

Set cookies on racks to cool completely.