Preheat the oven to 350F. Butter and flour a 9-inch cake pan. Place a piece of parchment paper that’s been trimmed to fit in the bottom.
Whisk together the flour, cocoa powder, baking soda, and salt in a medium bowl.
Whisk together the eggs, sugar, and brown sugar in a large bowl. Whisk in the oil, yogurt, and vanilla extract, and then whisk in the Guinness.
Add the dry ingredients to the wet and whisk to combine, being careful not to over-mix.
Pour the batter into the prepared pan and bake until a toothpick inserted in the center comes out clean, about 40 to 45 minutes.
Run a paring knife along the outside of the cake to loosen it from the pan. Turn the cake out onto a wire rack, let it cool for 5 minutes, and then peel off the parchment paper.
Cool the cake completely.
For the Frosting:
Once the cake is cool, make the frosting. Cream together the butter, cream cheese, and vanilla bean paste in a large bowl. Add the powdered sugar and use a hand-held electric beater to mix until smooth and creamy.
To Frost the Cake:
Place the cake on a cake plate or cake stand and top with the frosting, spreading it around. This makes enough frosting to frost the top and sides of a 9-inch cake, but I like to pile it on thick and only frost the top.
Notes
Storage: Store this cake wrapped in the fridge for up to 4 days.
Frosting Tip: To make this frosting even more special, I like to add ⅛ teaspoon almond extract and ⅛ teaspoon butter extract. I find that it simulates the flavor of Irish cream!