Preheat the oven to 160 degrees Celsius. Butter a 8 x 8 x 3 inch tin and line the bottom with baking parchment / paper. Set aside.
Measure the plain flour, baking soda and salt in a small bowl. Whisk the mixture with a wire whisk to distribute the baking soda and salt evenly.
In a small pot, measure the cocoa powder and sugar. Add in the coffee and butter. Heat the mixture on medium heat, and whisk frequently until all the butter has melted, and the cocoa powder and sugar has dissolved. Pour the cocoa-coffee into a large mixing bowl and let it rest for 10 minutes to cool down.
Stir in the Baileys. Crack in one egg into the cocoa-coffee mixture and whisk it in until it has been fully incorporated. Whisk in the second egg then whisk in the vanilla extract.
Sift in the flour mixture and whisk in gently until all the flour has been incorporated. The cake batter will be thin (very liquidy) and bubbly (because of the reaction between the baking soda and the cocoa powder). Pour the cake batter into the prepared tin. Lift up the tin and drop it on the table counter-top gently 3 to 5 times to remove excess air bubbles.
Bake the cake for 1h. Cover the top of the cake with aluminum foil and continue baking for 30 minutes until a skewer inserted into the centre of the cake come out with very little crumbs.Place the cake tin on a wire rack and let it cool completely.