Melt the butter and semisweet chocolate together over low heat, stirring until smooth. Remove from the heat and cool for 10 minutes.
Whisk the brown sugar, granulated sugar, egg, egg yolk, vanilla, and peppermint extract into the cooled chocolate mixture until glossy.
Add the flour, cocoa powder, baking powder, and salt. Mix just until combined, then fold in two-thirds of the mint chocolate pieces.
Refrigerate the dough for 20 minutes. Meanwhile, preheat the oven to 350 F and line two baking sheets with parchment paper.
Divide the chilled dough into 12 portions and arrange them at least 2 inches apart on the prepared baking sheets. Press the remaining mint chocolate pieces onto the tops.
Bake for 9 to 11 minutes, until the edges are set and the centers still look slightly underbaked. Cool on the baking sheets for 10 minutes before transferring to a cooling rack.