Add all-purpose flour, cocoa powder, espresso powder, baking powder, salt, and sugar in a large mixing bowl and whisk until well combined.
Add the melted butter, milk, eggs, and vanilla extract in a separate bowl and whisk until combined well.
Mix dry and wet ingredients and whisk until the batter is smooth and consistent.
Grease a cake tin with butter and line it with parchment paper. Pour the cake batter into the tin and smooth it into an even layer.
Prepare the Instant Pot, pour 2 cups of water, and place the trivet on top.
Carefully place the cake tin onto the trivet, ensuring it is level and not touching the sides of the pot.
Secure the Instant Pot lid and cook the cake on high pressure for 30 minutes.
Once the cooking time is ready, allow the pressure to release naturally for a few minutes before manually releasing any remaining pressure.
Carefully remove the cake from the Instant Pot using oven mitts or a pair of tongs. Let the cake cool in the tin for at least 20 minutes.
When the cake has cooled, remove it from the tin and slice it into pieces. Serve and enjoy!