Start by gathering all your ingredients and measuring them out.
In a medium-sized mixing bowl, combine the unsalted butter and the semi-sweet chocolate. Microwave in 20-second intervals, stirring in between, until fully melted and smooth.
Add the powdered sugar to the chocolate mixture and whisk until well combined. Then, add the large egg, egg yolk, pure vanilla extract, and espresso powder. Mix until evenly incorporated.
Gently fold in the all-purpose flour and salt until just combined.
Grease four ramekins with a little butter or cooking spray. Pour the batter evenly into each ramekin, filling them about 3/4 of the way full.
Pour 1 cup of water into the Instant Pot. Place a trivet inside and carefully position the ramekins on top of the trivet.
Seal the Instant Pot lid and set the valve to the sealing position. Cook on high pressure for 10 minutes. Allow for a natural release for 5 minutes before performing a quick release.
Carefully remove the ramekins from the Instant Pot. Let them cool for a minute before running a knife around the edges to loosen the cakes. Invert onto a plate and serve warm.
