Preheat your oven to 350°F (175°C) and grease the 9-inch round cake pan.
In a saucepan over medium heat, combine the stout and butter. Allow the butter to melt completely, then remove from heat.
Whisk in cocoa powder and sugar until well combined. Let the mixture cool for a few minutes.
In a separate bowl, beat the eggs and add in vanilla extract. Pour into the cooled stout mixture and stir until fully incorporated.
In another bowl, mix together the flour, baking soda, and salt. Slowly fold this dry mixture into the stout batter until just combined.
Pour the batter into the prepared cake pan and bake in the preheated oven for about 40 minutes, or until a toothpick inserted in the center comes out clean.
Allow the cake to cool in the pan for 10 minutes, then transfer to a cooling rack to cool completely.
For the frosting, beat together the cream cheese and heavy cream until smooth. Gradually add the powdered sugar and continue to mix until fluffy.
Once the cake is completely cool, frost it with the cream cheese mixture, spreading evenly over the top and sides.
Optional: For a richer flavor, consider adding chocolate chips to the batter before baking.
This cake can be made a day in advance and stored in the refrigerator before serving.
Optional: Add a drizzle of chocolate ganache on top for an extra touch of indulgence.