Gather all necessary ingredients before beginning.

Preheat the oven to 450°F. Generously grease four 6-ounce ramekins with butter, ensuring every surface is coated. Lightly dust them with flour, then tap out any excess. Arrange the prepared ramekins on a baking sheet and set aside.

Fill a medium saucepan with about an inch of water and bring it to a gentle boil over medium-high heat. Once boiling, lower the heat to maintain a simmer. Place the chopped chocolate and butter in a heatproof bowl and set it over the simmering water, ensuring the bowl does not touch the water. Stir occasionally, adjusting the heat as needed, until the chocolate and butter are fully melted and form a smooth, glossy mixture. This should take approximately 16 to 20 minutes. Remove from heat and set aside.

In a separate bowl, combine the eggs, egg yolks, sugar, and salt. Using an electric mixer fitted with a whisk attachment, beat the mixture on high speed for 2 to 3 minutes until it becomes pale, thick, and airy.

Give the melted chocolate mixture a final whisk to ensure it remains smooth. Gently fold the warm chocolate and the flour into the whipped egg mixture, stirring just until no streaks remain and the batter is fully incorporated.

Evenly divide the batter among the prepared ramekins, filling each about halfway. Use a small offset spatula to smooth the tops if needed.

Transfer the baking sheet with the ramekins to the preheated oven. Bake for 9 to 12 minutes, or until the tops of the cakes are just set, the edges spring back when lightly touched, and the centers remain soft.

Once out of the oven, let the cakes rest in their ramekins on the baking sheet for about 1 minute. To unmold, carefully invert a dessert plate over each ramekin, then flip it over in one swift motion. Let it sit for 10 seconds before gently lifting the ramekin away. Repeat for the remaining cakes.

Serve immediately while warm, allowing the molten center to flow with the first spoonful.