Step 1

Preheat the oven to 350°F and line an 8-inch springform pan with parchment paper.

Step 2

Place the Guinness into a small saucepan and place it over medium heat. Cut the butter into eight to ten slices and add them to the pot. Heat the beer and butter, whisking frequently, until the butter has completely melted.

Step 3

Whisk the cocoa powder and 1/2 cup of the sugar into the Guinness mixture. Let the mixture cool to room temperature (Note 1).

Step 4

While the Guinness mixture cools, stir the water and ground flaxseeds together in a large mixing bowl. Let the mixture sit for about five minutes, until it thickens and gels.

Step 5

Once the flax mixture has gelled, add the remaining cup of granulated sugar to the bowl, along with the brown sugar, yogurt, and vanilla. Beat the ingredients together using an electric mixer on high-speed for about one minute, until the ingredients are fully blended and slightly foamy.

Step 6

Pour the cooled Guinness mixture into the bowl with the flax mixture. Whisk the ingredients together.

Step 7

Begin whisking the flour into the bowl with the wet ingredients. Add about a half cup at a time, whisking in each addition before adding more flour. When you add the last bit of flour, sprinkle the baking soda and salt over the flour before whisking everything together. Make sure to fully mix the batter, but don't overdo it.

Step 8

Pour the batter into the prepared springform pan.

Step 9

Bake the cake for 55 to 60 minutes, until a toothpick inserted into the middle comes out clean.

Step 10

Place the cake on a cooling rack when it's done baking. Allow the cake to cool completely before removing it from the pan.

Step 11

Slather a layer of frosting over the top of the cake. Slice and serve.