Preheat your oven to 400°F (200°C). Generously butter the inside of two 6-ounce ramekins. Dust them with cocoa powder or all-purpose flour, tapping out any excess. This helps prevent sticking and gives a nice finish.

In a small heatproof bowl set over a saucepan of simmering water (ensure the bowl doesn't touch the water), or in a microwave-safe bowl (heated in 30-second intervals), melt the 4 tablespoons of unsalted butter and chopped dark chocolate together. Stir until completely smooth and combined. Remove from heat and let cool for about 5 minutes.

In a medium mixing bowl, whisk together the powdered sugar, large egg yolk, whole egg, pinch of salt, and vanilla extract until the mixture is light in color and slightly frothy.

Gradually pour the slightly cooled chocolate and butter mixture into the egg mixture, whisking constantly until everything is well combined and forms a smooth batter.

Gently fold in the 2 tablespoons of all-purpose flour using a rubber spatula. Mix just until no dry streaks of flour remain; be careful not to overmix, which can make the cakes tough.

Divide the batter evenly between the two prepared ramekins. Place the ramekins on a small baking sheet (this makes them easier to transfer in and out of the oven). Bake for 12-14 minutes. The cakes are done when the edges are set and puffy, but the center still jiggles slightly when gently shaken. The very center should look moist and slightly undercooked for that signature lava effect.

Carefully remove the ramekins from the oven. Let them cool for just 1-2 minutes. Run a thin knife around the edge of each cake, then invert each onto a dessert plate. Serve immediately, optionally garnished with a dusting of powdered sugar, a scoop of vanilla ice cream, or fresh berries.