Gather all your ingredients and ensure the butter and chocolate are at room temperature for easy melting.
In a microwave-safe bowl, combine the chopped chocolate and cubed butter. Microwave in 30-second intervals, stirring in between, until melted and smooth. Let it cool slightly.
In another bowl, whisk together the powdered sugar, flour, salt, and espresso powder.
In the bowl with the melted chocolate and butter, add the whole egg, egg yolk, and vanilla extract. Whisk until well combined.
Gradually add the dry ingredients to the chocolate mixture, stirring gently until just combined. Be careful not to overmix.
Grease four ramekins with butter or non-stick spray. Divide the batter evenly among the ramekins.
Pour 1 cup of water into the bottom of the Instant Pot. Place the trivet inside the pot.
Place the filled ramekins on the trivet. Secure the lid and set the Instant Pot to cook on high pressure for 10 minutes. Quick-release the pressure when done.
Carefully remove the ramekins from the pot. Let them cool for a minute, then run a knife around the edges and invert onto a plate. Serve immediately, perhaps with a scoop of vanilla ice cream or a dollop of whipped cream for the ultimate treat!