Preheat oven to 350F and grease a 9” cake pan (a springform works well if that is all you have), set aside.
Heat Baileys on low in a small saucepan then stir in cocoa and espresso powder (it will be thick). Allow it to cool slightly.
In a medium bowl, whisk all-purpose flour, light brown sugar, white sugar, cornstarch, baking soda, sea salt and baking powder. Set aside.
In a large mixing bowl, whisk Greek yogurt, vegetable oil, egg, milk, vanilla and vinegar. Lastly, add in the Baileys mixture.
Add dry ingredients to the large bowl and mix well.
Transfer cake batter to your prepared pan and bake for about 22-25 minutes (a toothpick should show moist crumbs from the center). Leave it to cool for about 15 minutes then carefully flip onto a parchment covered wire rack.
Make your frosting once the cake is cool enough, by adding everything to a stand mixer and run on medium low until well combines and smooth.
Carefully remove parchment paper and place cake on a lightly sugar covered platter (if desired). Spread on with an offset spatula and enjoy.