For the Cookies:
16 tablespoons unsalted butter, room temperature
1 cup light brown sugar, packed
1 cup granulated sugar
2 large eggs, room temperature
2 tablespoons stout beer, room temperature
1 tablespoon real vanilla extract
1 cup bread flour
1 cup all-purpose flour
⅔ cup unsweetened dark (Dutch process) cocoa powder
1½ teaspoons baking powder
1 teaspoon baking soda
1 teaspoon sea salt
For the Buttercream:
2½ cups powdered sugar
8 tablespoons unsalted butter, room temperature
3 tablespoons Irish cream liqueur
1. Preheat the oven to 350°F and place a rack in the top third of the oven, at least 6 inches from the heat source. Cover several baking sheets with parchment paper.
2. In an electric stand mixer fitted with the paddle attachment, add the butter, brown sugar and granulated sugar and mix on medium for 4 minutes, or until light and fluffy. With the mixer on low, add the eggs one at a time, making sure one is well blended before adding the next. Add in the beer and vanilla and mix for 1 minute more.
3. In a medium bowl, whisk together the bread flour, all-purpose flour, cocoa powder, baking powder, baking soda and sea salt. Add to the butter mixture and mix on low until just combined. Make 1½-tablespoon balls; this dough is sticky, so use a cookie scoop or two spoons. If the dough is too sticky to handle, chill in the fridge for 1 hour or so until firmed up. Leave 3 inches between the dough balls and place on the prepared baking sheet. Chill the balls in the freezer for 10 minutes or the refrigerator for 20 minutes.
4. Take the cookies from the freezer directly to the oven and bake one sheet at a time in the top third of the oven for 11 minutes. Let cool on the baking sheet for 5 minutes and then transfer to a rack to cool completely.
5. To make the buttercream, in an electric stand mixer fitted with the paddle attachment, mix the powdered sugar, butter and liqueur on medium for 4 minutes or until smooth. Smear some on the top of each cookie and serve.