Preheat your oven to 425°F (220°C). Generously grease two 6-ounce ramekins with butter, making sure to coat the bottoms and sides. Dust them lightly with cocoa powder, tapping out any excess.
Add the chopped semi-sweet chocolate and butter to a heatproof bowl. Microwave in 20-second intervals, stirring between each interval, until the mixture is smooth and completely melted. Alternatively, melt them together in a heatproof bowl set over a saucepan of gently simmering water.
In a separate bowl, whisk the whole egg, egg yolk, and granulated sugar for about 1–2 minutes, until the mixture looks slightly lighter and the sugar begins to dissolve. Whisk in the vanilla extract and salt.
Slowly pour the melted chocolate mixture into the egg mixture, whisking continuously until everything is combined. Add the flour and gently fold it in with a silicone spatula until no dry streaks remain.
Divide the chocolate batter evenly between the prepared ramekins. Gently tap each ramekin on the counter to release any large air bubbles.
Place the baking sheet in the preheated oven and bake for 10–12 minutes. The edges should look set, while the centers should remain soft and slightly jiggly.
Ovens and ramekin materials can affect baking time, so start checking at 10 minutes. Baking them too long can cause the centers to set completely instead of staying molten.
If you prefer to unmold them, carefully run a thin knife around the edges, place a dessert plate over each ramekin, and invert it. Let the ramekin sit upside down for a few seconds before lifting it away.
Dust with powdered sugar and serve immediately with vanilla ice cream or fresh berries. Break into the center with a spoon to enjoy the warm, flowing chocolate filling.