Prepare a 7-inch springform pan by spraying generously with non-stick spray and add a round of parchment paper in the bottom of the pan and set aside.
Add ½ cup water into a microwave safe bowl and place in the microwave for 1 minute.
In the bowl of a stand mixer, equipped with a whisk attachment, add the flour, sugar, cocoa powder, baking powder, baking soda, espresso powder and salt. Whisk until all ingredients are combined.
Slowly pour in the milk, melted butter, egg, and vanilla extract into the dry ingredients and mix until there are no dry spots. Do not overmix.
With the mixer on low speed, slowly pour in the hot water and mix on low until fully combined. Increase the speed to high for about 1 minute.
Lay out a large piece of aluminum foil and place the springform on top. Pour the cake batter into the springform and cover the entire pan in foil. Use two pieces if needed.
Pour 1 ½ cups of water into the bottom of the inner pot of your pressure cooker and place a trivet in the bottom. Place the springform on top of the trivet and place the lid on "sealing".
Set your pressure cooker on high manual pressure for 50 minutes. Allow to naturally release for 12 minutes then manually release any remaining pressure.
Remove the cake form the inner pot and place on a wire rack. Immediately remove the foil and allow to cool completely.
Once the cakes are cool, place in the refrigerator and prepare the frosting.