Add all dry ingredients to large mixing bowl – flour, cocoa powder, and salt. Note: We do not consider sugar to be a dry ingredient since it melts. Using a whisk (or fork), mix until fully combined.
In a separate mixing bowl, begin adding wet ingredients – starting with sugar and butter. Using a hand mixer, blend them together until light and fluffy. Then add eggs, vanilla, and vinegar and blend until fully incorporated, making sure to scrape sides of the bowl. Add red food coloring and Kahlua and mix again.
Pour dry ingredients into bowl with wet ingredients then mix just until fully combined. Do not over-mix! I recommend stopping the hand mixer sooner than later and switching to a rubber spatula.
Spray 7-inch cheesecake or springform pan with nonstick cooking spray. Place pan on a surface that won’t be damaged if red color touches it. Pour batter into pan and cover with aluminum foil.
Place 3-inch trivet into pot, along with 1 1/2 cups of water. Then place pan on top of trivet. Lock lid and cook at high pressure for 75 minutes. Once cook time is complete, allow pressure to release naturally for 10 minutes, then release remaining pressure.
Remove push pan, uncover, and let cool for at least 10 minutes before removing cake. Then, once pan is warm to touch, push out cake to a cooling rack and let cool completely before icing.
Meanwhile - Place the butter, cream cheese, and 1 mini bottle of Baileys in a mixing bowl and mix together on medium speed for a few minutes, until creamy. Slowly add the powdered sugar a little bit at a time. Lastly, increase to the highest speed until whipped texture is achieved.
When it’s time to add the frosting to the cake, place big spoonfuls in the middle of the top of the cake. Then gently spread outwards. Since the frosting is so soft, you should be able just let it fall over the sides. Once the cake is iced, place in the fridge for 30 minutes so that the frosting sets.