Preheat your oven to 425°F (220°C). Grease six ramekins thoroughly with butter and lightly dust with cocoa powder to prevent sticking. Set aside.
In a small saucepan over low heat, melt the unsalted butter. Once melted, remove from heat and whisk in the unsweetened cocoa powder until smooth and glossy.
In a medium bowl, combine the whole eggs, egg yolks, granulated sugar, salt, and vanilla extract. Using a whisk or electric mixer, beat the mixture until it becomes thick, pale, and slightly frothy.
Slowly add the melted cocoa butter mixture into the egg mixture, stirring constantly to incorporate. Then fold in the all-purpose flour gently, just until combined. Be careful not to overmix.
Spoon the batter evenly into each prepared ramekin, filling them about two-thirds full. Create a small well in the center of each cake and drop a tablespoon of caramel sauce inside. Cover the caramel with a little more batter.
Place the ramekins on a baking sheet and bake for 12-14 minutes. The edges should look set while the center remains soft and slightly jiggly.
Remove from the oven and let the cakes cool for 2-3 minutes. Carefully run a knife around the edges to loosen them, then invert onto serving plates. Sprinkle with a pinch of flaky sea salt immediately before serving for that perfect salty-sweet contrast.