Prep the ramekins. Grease 4 to 6 heatproof ramekins (6-ounce size works well) with butter.
Dust lightly with cocoa powder, tapping out the excess. This helps the cakes release cleanly.
Melt chocolate and butter. In a microwave-safe bowl or over a double boiler, melt the chocolate and butter together until smooth. Stir gently and let it cool for 2–3 minutes so it’s warm but not hot.
Whisk the eggs and sugars. In a separate bowl, whisk the granulated sugar, brown sugar, 2 eggs, and 2 yolks until glossy and slightly thick, about 30–45 seconds.
Add the vanilla and stir.
Combine the mixtures. Slowly pour the warm chocolate mixture into the egg mixture, whisking constantly. You want everything fully combined and silky.
Add dry ingredients. Sift in the flour, cocoa powder, salt, and espresso powder if using. Fold gently with a spatula until just combined.
Do not overmix.
Fill the ramekins. Divide the batter evenly among the prepared ramekins, filling each about 3/4 full.
Set up the pressure cooker. Add 1 cup of water to the pot. Place a trivet inside. Arrange the ramekins on the trivet.
If stacking, place a small piece of foil or a rack between layers to keep them level. Loosely tent the tops with foil to prevent water droplets from landing on the batter.
Pressure cook. Seal the lid and cook on High Pressure for 7–9 minutes for a molten center. Thicker ramekins or a larger single dish may need up to 10 minutes.
The edges should be set, with a soft, jiggly center.
Quick release. When the timer ends, perform a quick release. Carefully remove the ramekins with tongs. Rest them for 1–2 minutes; the carryover heat will finish setting the edges without cooking the center.
Serve. Run a thin knife around the edges and invert onto plates, or serve directly in the ramekins.
Dust with powdered sugar and add a scoop of vanilla ice cream or a drizzle of lightly whipped cream.