For the ice cream: Combine the cream, milk and vanilla in a heavy-bottom pan and bring to just under a boil to steep. Whisk together the sugar, espresso powder, salt and egg yolks in a bowl. Gently pour about one-third of the hot milk mixture into the sugar/yolk mixture to temper, whisking until smooth. Pour this tempered mixture into the remaining hot milk mixture, again whisking until smooth. Return the saucepan to medium-low heat, stirring gently and constantly until it starts to just thicken a bit into a custard or reaches 175 degrees F.
Remove from the heat and whisk in the beer. Strain the custard through a fine mesh strainer, and chill completely over an ice bath. Once chilled, follow the instructions on your home ice-cream maker and make the custard into an ice cream. When it is done, gently fold in the chopped dark chocolate bits. Freeze to set, at least 3 to 4 hours.
For the cookies: Preheat the oven to 325 degrees F. Sift together the flour, baking powder, baking soda and salt. Beat the sugar and butter together in the bowl of a stand mixer with a paddle on medium speed until light and creamy. Add the eggs one at a time and the vanilla, beating until combined, scraping down the sides as needed.
Add the blended flour mixture, mixing until everything just comes together. Scoop 1-tablespoon balls of dough onto baking sheets, spacing about 2 inches apart. Gently press the dough balls flat using the bottom of a glass or measuring cup. Mix together the sugar and cinnamon and lightly sprinkle on top of the cookies.
Bake for 8 to 10 minutes, rotating the baking sheets halfway through. Let cool to allow the cookies to firm before removing from the sheets.
To assemble ice-cream sandwiches, scoop one large scoop of ice cream onto the bottom of a cooled snickerdoodle. Top with another cookie, right-side up.
NotesCook's Note: Be careful not to over-mix the cookie dough.
This recipe was provided by a chef, restaurant or culinary professional and makes a large quantity. The Food Network Kitchens chefs have not tested this recipe, in the proportions indicated, and therefore, we cannot make any representation as to the results.