Using a stand mixer fitted with the paddle attachment, cream together the softened butter and powdered sugar until light and fluffy.
Then add in the vanilla extract and peppermint extract and mix until fully combined.
Mix in the flour, cocoa powder, and salt until just combined. The dough should come together into a soft but not sticky ball.
Divide in half and press the dough into discs. Wrap tightly in plastic wrap and refrigerate overnight (or a minimum of at least 2 hours).
Line a baking sheet with parchment paper.
On a lightly floured surface, roll out the dough ¼ inch thick and cut into your desired shaped. Place cutout cookies 1-2 inches apart on your baking sheet (they won’t spread much).
Place the baking sheet in the freezer for a minimum of 20 minutes (or the fridge for 40 minutes) before baking to allow the cookies to firm back up. This ensures the cookies won't spread during baking.
While the cookies are chilling, preheat your oven to 350°F.
Bake for 9-11 minutes or until the edges are set. Bake on the middle rack of the oven and rotate the pan halfway through baking for the best results.
Let the cookies cool on the baking sheet for 2-3 minutes, then remove and let them finish cooling on a cooling rack.
Let the cookies cool completely before decorating.
Dip the cookies halfway (or more, you do you) into the melted white chocolate and place back on the cooling rack. Sprinkle with crushed peppermint before the chocolate cools and hardens.
Let the chocolate harden completely before removing from the cooling rack.
Notes
Store cookies in an airtight container at room temperature for up to a week.