Make the dough: Cut butter into three pieces (around 2 tablespoons each) and add to bowl of an electric mixer fitted with paddle attachment.

If using a bar of chocolate, chop it into ¼- to ½-inch chunks. Break mint candies into similar sized chunks by centering them in a kitchen towel placed on a cutting board. Fold fabric edges completely over mints to cover and use a rolling pin to rap from one side to the other.

Sift flour, cocoa and baking soda into a small mixing bowl. Add salt and whisk to combine. Pile chocolate and mints on top.

Add sugars, mint oil and espresso to butter in mixer bowl. Beat on medium-high to combine, 3 minutes. Mixture should look uniformly cardboard-colored and sandy. Use a rubber spatula to scrape around sides and bottom of bowl to be sure everything is evenly distributed, and beat briefly to incorporate any missed bits. Scrape and beat once more. Turn off mixer.

Dump dry ingredients along with chocolate and peppermint over butter mixture, followed by egg. With paddle on low speed, run mixer to begin to integrate ingredients, increase speed to medium-high to fully incorporate and then to high speed for the last few seconds.

Scrape dough onto a floured board and shape and roll into a 12-by-1½-inch log. Wrap in plastic and freeze 1 hour or refrigerate overnight to set. (Tightly wrapped in plastic, the dough will keep up to 2 months.)

Preheat oven to 350 degrees and line two baking sheets with parchment paper. If dough is in freezer, remove and let sit to thaw slightly, 2-3 minutes. (It’s easier to slice when firm).

In a small bowl, stir together sugar and salt. Use scissors to cut frozen marshmallows in half crosswise.

Slice dough into ¼-inch rounds and space 1½ inches apart on prepared pans. Sprinkle each with ¼ teaspoon sugar-salt mixture and place a marshmallow half on top, cut side down.

Bake until cookies crack and fall slightly, and marshmallows are toasted and gooey, 12-14 minutes. Let cool on baking sheets 5 minutes, then transfer cookies to a cooling rack. Eat warm or at room temperature. Cookies keep in an airtight container up to 5 days.