Spray two 6-oz ramekins with nonstick baking spray.
Add the butter and chocolate to a small microwave-safe bowl. Microwave for 1 minute. Whisk the butter and chocolate together until combined. If the chocolate has not fully melted, microwave it for an additional 30 seconds.
Whisk the egg and egg yolk into the butter and chocolate mixture.
Add the powdered sugar, flour, vanilla, salt, and espresso powder. Whisk to combine.
Divide the batter between the ramekins.
Insert the trivet into the Instant Pot. Add just enough water so that the water line reaches the height of the trivet (in a 6-Qt. Instant Pot, it is about 1 ¾ cups).
Place the ramekins on top of the trivet.
Close the lid and ensure the valve is in the sealing position. Set the Instant Pot to Pressure Cook for 11 minutes with Manual release.
When the Instant Pot has finished cooking, release the pressure manually by switching the valve to the venting position. Be careful, it will steam!
Remove the ramekins from the Instant Pot with an oven mitt and run a sharp knife around the edge between the ramekin and the cake. Then, allow the cakes to set for 2 minutes.
Invert the cake onto a plate and garnish with powdered sugar, whipped cream, ice cream, or fresh berries. Serve immediately.