In a medium saucepan over medium-high heat, reduce the Guinness and the brown sugar, stirring occasionally to prevent scorching, until thick and syrupy and measures ⅓ cup, about 30-45 minutes. Set aside to cool slightly.
In a medium bowl, whisk together the flour, cocoa, espresso powder, baking powder, baking soda, and salt; set aside.
In the bowl of a stand mixer fitted with the paddle attachment, cream the butter and sugars until light and fluffy, about 3 minutes. Add the eggs and yolk, one at a time, until combined. Scrape down the sides of the bowl. Add the vanilla and mix until combined. With the mixer on low, gradually add the cooled beer syrup, mixing until combined. Gradually add the dry mixture until no flour is visible. Fold in both the white and milk chocolate chips.
Cover the bowl with plastic wrap and refrigerate until firm, about 3 hours, preferably overnight. Well wrapped or stored in an airtight container, dough will keep in the refrigerator for up to 3 days. To freeze, scoop the dough into portions and place on a parchment lined baking sheet. Freeze until firm, then place in a freezer safe plastic bag for up to one month.
Preheat the oven to 325°F. Line a large baking sheet with parchment paper. Using a 1-ounce ice cream scoop (about 2 tablespoons), scoop out portions of the cookie dough onto the prepared baking sheet spaced 3 inches apart. Bake the cookies until the edges are set, about 15-17 minutes (a minute or two more if frozen). Allow the cookies to cool on the baking sheet for 2 minutes, then transfer to a wire rack to cool completely. Enjoy!