Prepare the Cookie Dough : Preheat your oven to 350°F (175°C). Line two baking sheets with parchment paper or silicone baking mats. In a medium bowl, whisk together the flour, cocoa powder, baking soda, and salt. Set aside. In a large mixing bowl, cream together the softened butter, granulated sugar, and brown sugar until light and fluffy (about 2 minutes). Beat in the eggs, one at a time, followed by the vanilla and peppermint extracts.
Combine Wet and Dry Ingredients : Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Be careful not to overmix, as this can make the cookies tough.
Shape and Bake : Using a cookie scoop or tablespoon, scoop the dough into 1 1/2-inch balls and place them on the prepared baking sheets about 2 inches apart. Bake for 8–10 minutes, or until the edges are set and the centers are slightly soft. Let the cookies cool on the baking sheets for 5 minutes before transferring them to a wire rack to cool completely.
Melt the White Chocolate : In a microwave-safe bowl, melt the white chocolate in 20-second intervals, stirring in between, until smooth and glossy.
Dip and Decorate : Dip half of each cooled cookie into the melted white chocolate, letting the excess drip off. Place the dipped cookies back on the parchment paper and immediately sprinkle with peppermint bits before the chocolate sets. Let the cookies sit at room temperature or in the fridge until the white chocolate hardens.
Serve and Store : Serve these festive cookies immediately, or store them in an airtight container at room temperature for up to 1 week.