Lightly grease the insides of your ramekins using a small reserved piece of the 1/4 cup unsalted butter; set the greased ramekins aside.
Pour 1 cup water into the Instant Pot and place the trivet inside.
In a microwave-safe bowl, add the remaining cubed butter and the 4 oz. semi-sweet (or dark) chocolate.
Microwave in 15-second intervals, stirring or whisking between intervals, until the butter is melted and the chocolate is fully smooth.
Whisk in 1/2 cup powdered sugar and 1/4 teaspoon espresso powder until the mixture is thick and smooth.
Add 1 large egg, 1 egg yolk, and 1/2 teaspoon vanilla extract; whisk until fully combined.
Add 1/4 cup all-purpose flour and 1/4 teaspoon salt. Fold in gently with a spatula just until incorporated—do not overmix.
Divide the batter evenly among the prepared ramekins.
Place the ramekins on the Instant Pot trivet, close the lid, and set the valve to the “sealing” position.
Cook on High Pressure for 8 minutes.
When the timer finishes, press “Cancel/Off” and perform a quick pressure release by carefully moving the valve to “venting.” Wait until the float valve drops, then open the lid.
Using oven mitts, remove the ramekins from the Instant Pot and let them rest in the ramekins for 1–2 minutes.
To unmold each cake, cover the ramekin with a plate, invert and tap gently, then lift the ramekin off the cake.
Dust the cakes with powdered sugar and serve immediately.