Preheat the oven to 350° F. Line a baking sheet with parchment paper or a silicon baking mat.
In a medium mixing bowl, combine the flour, baking powder and salt; stir briefly with a fork to combine. In the bowl of a stand mixer fitted with the paddle attachment, beat together the butter and sugar on medium-high speed until well combined, about 2 minutes. Beat in the eggs one a time, mixing well after each addition. Add in the dry ingredients and mix on low speed just until incorporated. Fold in the 2/3 cup crushed peppermints and chocolate chips with a rubber spatula until evenly incorporated.
Evenly divide the dough into 4 portions. Form each into a 9″ by 1½” log on the prepared baking sheet, spaced evenly. Bake until the cookies are light golden brown on top, about 18-20 minutes. Remove the pan from the oven and let cool for 10 minutes on the cookie sheet. Reduce the oven temperature to 325° F.
After the logs have cooled for 10 minutes, use a sharp serrated knife to cut the logs into ½-inch slices on the diagonal. Arrange the cut pieces on the baking sheet, laying on one of their cut sides so one cut side is facing up. Bake for 15 minutes more, until the cookies are light golden brown and crisp. (They may seem a bit soft, but will firm as they cool.) Transfer to a cooling rack to cool completely.
Once the biscotti have cooled, garnish with melted chocolate and crushed peppermint. Let stand at room temperature until the chocolate has set completely. Store in an airtight container.