Whisk the flour, cocoa powder, baking soda, and salt together in medium bowl. Set aside.

In a large bowl using a handheld or stand mixer fitted with a paddle attachment, beat the butter, brown sugar, and 1/3 cup (67g) granulated sugar together on medium-high speed until smooth and creamy, about 2 minutes. Add the egg, vanilla extract, and peppermint extract and beat on high speed until combined, about 1 minute. Scrape down the sides and up the bottom of the bowl and beat again as needed to combine. Pour the dry ingredients into the wet ingredients, add the milk, and mix on low until combined. The cookie dough will be thick.

Roll balls of dough, a little less than 1 Tablespoon each (about 1 inch balls), and roll each into remaining 1/3 cup (67g) granulated sugar. Place dough balls onto a large lined baking sheet. Using your thumb or the end of a spatula (see post above), make an indent into each cookie. If you find that the balls are cracking when you make an indent, use your hands to push back together. (Some cracks are bound to happen as the cookies expand in the oven—see my photos. No worries there!)

Chill the shaped cookies for at least 2 hours in the refrigerator or 1 hour in the freezer (or up to 4 days in the refrigerator). Cover them if chilling for longer than 3 hours.

Preheat oven to 350°F (180°C). Line a baking sheet with parchment paper or a silicone baking mat. Remove chilled and shaped cookies from the refrigerator. Divide between both baking sheets, spacing the cookies about 2-3 inches apart. This recipe yields about 30 cookies, so you’ll have a 3rd batch with only a few cookies on the sheet.

Bake for 12-14 minutes or until the edges are set. The cookies will still look and feel a little soft. Remove from the oven. The indents will have lost some shape or have puffed up, so use the end of a spatula to make an indent again into the warm cookies.

Allow cookies to cool on the baking sheets for 5 minutes, then transfer to a wire rack to cool completely before filling with ganache.

Place chocolate into a heat-proof bowl. Heat the cream in a small saucepan until it begins to gently simmer. (Do not let it come to a rapid boil—that’s too hot!) Pour over chocolate and let it sit for 2-3 minutes to gently soften the chocolate. Slowly stir until completely combined and chocolate has melted. Stir in the peppermint extract. Taste and add another drop if desired. (It’s potent so don’t go overboard!) Allow to cool for at least 10 minutes before spooning into cookies.

Spoon 1/2 – 1 teaspoon of ganache into each indentation. I fit about 3/4 teaspoon into each. Sprinkle ganache with crushed candy canes. Ganache will thicken inside the cookies and set on the tops after a few hours, but will still be creamy when you bite into the cookies.

Cookies stay fresh covered at room temperature for up to 3 days or in the refrigerator for up to 1 week.