Combine the bittersweet or semisweet chocolate, unsalted butter, and unsweetened chocolate in a large saucepan.
Over low heat, stir the chocolate and butter occasionally until they are well combined and smooth.
Finely crush the peppermint candies.
Remove saucepan from heat once the chocolate and butter are melted and add crushed peppermint candies and sugar.
Cool mixture for 10-15 minutes.
Add in one egg at a time and whisk.
Whisk in peppermint extract and vanilla extract.
In a small bowl, mix baking powder, flour, and salt with a rubber scraper.
Add the dry mixture to wet mixture and combine.
Add the chocolate chips and mix to combine.
Cover batter and chill for at least 3 hours or overnight. The batter should be firm yet malleable.
Move oven rack to the center and preheat oven to 325 degrees.
Cover a baking sheet with either parchment paper or silicone baking mat. Scoop batter with a tablespoon and roll into a ball with your palms. Place cookie batter balls on the baking sheet and space about 1-2 inches apart.
Bake on the center oven rack for 11 minutes.
Remove and let sit for 3-5 minutes.
Press coarsely crushed peppermint candies into the center of the cookies or sprinkle powdered sugar on top.
Transfer to a cooling rack and cool completely.
Place into a covered storage container and store in refrigerator or freezer.