Pour the Guinness into a small saucepan and place it over medium heat. Bring the Guinness to a low boil, then lower the heat and let it simmer until it reduces to about ½ cup, about 20 minutes (Note 1). Let the Guinness cool until it's just barely lukewarm or cooler (Note 2). You can start to prepare your other ingredients while the Guinness cools.
Preheat the oven to 350°F and line the bottom and sides of a 9 x 9 inch baking pan with parchment paper. Leave a little overhang, which you'll later use to remove the brownies from the pan.
Whisk the non-dairy milk and ground flaxseed together in a small bowl. Let the mixture sit for at least five minutes, to gel.
While the flax mixture sits, place the butter and chocolate chips into a large, microwave-safe mixing bowl. Microwave them in 30 second increments, stirring in between, until they're completely melted and smooth. It should only take about two or three zaps (Note 3).
Whisk the reduced Guinness into the melted chocolate mixture, followed by the oil, flax mixture, sugar, brown sugar, and vanilla extract.
Add the flour, then sprinkle the cocoa powder, cinnamon (if using), baking soda, and salt over the flour. Whisk just until the ingredients are combined.
Pour the batter into the prepared baking pan. Bake the brownies for 30 to 35 minutes, until a toothpick inserted into the center comes out clean.
Place the pan on a cooling rack and let the brownies cool completely.
Once the brownies are cool, remove them from the pan by gently pulling upwards on the excess parchment paper.
Optionally, frost the brownies. Cut them into squares.
Serve.