Prep:
Preheat oven to 425°F (220°C). Grease six wells of a nonstick muffin pan or six 6-oz ramekins generously with butter and dust with cocoa powder (helps release the cakes cleanly).

Brown the butter:
In a saucepan over medium heat, melt the butter and cook 3–5 minutes until golden and nutty. Immediately remove from heat and stir in the chopped chocolate until melted and smooth. Cool for 2–3 minutes.

Make the batter:
In a large bowl, whisk together eggs, yolks, vanilla, and powdered sugar until glossy and slightly thickened (about 30 seconds).
Add flour, salt, and espresso powder (if using); whisk to combine.
Slowly pour in the warm chocolate-butter mixture while whisking until smooth and shiny.

Fill the pan:
Divide batter evenly among the prepared wells, filling about ¾ full.

Bake:
Bake 8–9 minutes, just until edges look set and the centers are still soft and slightly jiggly. Do not overbake!

Invert & serve:
Let sit 1–2 minutes, then run a knife around the edges and invert onto serving plates. Serve immediately with ice cream or powdered sugar.