Combine the stout and vanilla pod and seeds in a large, heavy-bottomed saucepan. Over a medium-high flame, bring to a simmer. Cook, swirling occasionally, until reduced to 1 cup. (Check by pouring into a heat-proof measuring cup.) This will take around 20 minutes. (If you accidentally reduce the stout too much, make up the difference with more stout.) Cool the stout slightly. Remove the vanilla pod and discard.
Make the ice cream:
Warm the half and half in a medium saucepan set over a medium flame, swirling occasionally, until steaming. Meanwhile, whisk together the sugar, egg yolks, and salt in a medium bowl. Set the bowl on a damp kitchen towel. When the half and half is warm, slowly drizzle half of it into the egg yolk mixture while whisking constantly. Pour the mixture back into the pot and cook over low heat, stirring constantly with a heat-proof silicone spatula, until the mixture thickens slightly and/or registers 170º on an instant-read thermometer, a few minutes.
Remove from the heat and immediately add the brown sugar and stout reduction, stirring to dissolve the sugar, then stir in the cold heavy cream. Strain the mixture through a fine-mesh sieve, and chill until very cold, at least 4 hours, preferably overnight, or up to 2 days.
When the mixture is very cold, place it in the freezer for 30 minutes to get it even colder, giving it a stir every 10 minutes. (This ensures a dense ice cream, but you can skip this step if you prefer.) Churn the mixture in an ice cream maker according to the manufacturer's instructions. Transfer it to an airtight container and freeze until firm, at least 2 hours or up to several weeks.
Make the cookies:
In a large bowl, whisk together the melted butter, vegetable oil, sugars and eggs. Whisk in the stout reduction. In a medium bowl, whisk together the flour, salt, and baking soda. Add the flour mixture to the butter mixture along with the oats, chocolate, pecans, and cacao nibs. Stir until just combined. Cover the bowl and let stand at room temperature for an hour.
Position racks in the upper and lower thirds of the oven and preheat to 325ºLine 2 cookie sheets with parchment paper. Scoop the dough into 1 1/2" balls (I use a #40 spring-loaded ice cream scooand place the balls at least 2" apart on the lined cookie sheets. Top each with a few flecks of flaky salt.
Bake the cookies until they are golden around the edges and set on top, 10-12 minutes, rotating top to bottom and front to back halfway through baking. Let cool completely. (Optionally, freeze the cookies before making the sandwiches; this makes them a little easier to handle, and helps to keep the ice cream cold. Layer the cookies between sheets of parchment paper in an airtight container to prevent them from sticking.)
Assemble the sandwiches:
First, separate your cookies into matching pairs of approximately the same size and shapes. Working quickly and in batches, use a spring-loaded ice cream scoop (#24) to scoop scoops of ice cream onto the flat side of a cookie. Top with another cookie, and place in the freezer. Work quickly to prevent your ice cream from melting, using all the cookies and ice cream.
Store the sandwiches in a freezer-safe container either layered with parchment paper to prevent sticking, or wrapped individually with plastic wrap. The cookies should keep for up to a month.
These sandwiches have beer in both the cookies and the ice cream. Thirty ounces of stout are simmered with a vanilla bean until reduced to one cup; half goes into the cookies and half into the ice cream. Start this project at least 1 day ahead to give the ice cream ample time to freeze. Use a rich, creamy stout or porter here; I used Bison's Organic Chocolate Stout.The cookies are sensitive to small variations in temperature. If your oven runs hot, they may not spread enough to make them into sandwiches. I recommend baking a tester or two to make sure you get the right spread; if they spread too much, increase the oven temperature. Too little, turn it down a notch. For more cookie baking tips and tricks, see my post on Soft and Chewy Gluten-Free Chocolate Chip Cookies.Variation: Thick and Chewy Chocolate Stout Oatmeal Cookies I like this version better when making the cookies to have on their own. They don't spread enough to become sandwiches, but their flavor is milder, and their texture more toothsome. I brought these to a party, and people went mad for them. Omit the vegetable oil and replace it with the same amount of butter. Increase the barley flour to 1 3/4 cups.Nutritional values are based on one of twenty four ice cream sandwiches.