01 - In a saucepan over medium heat, combine granulated sugar and water. Cook without stirring until the mixture turns amber in color, about 8 to 10 minutes. Remove from the heat and whisk in heavy cream, unsalted butter, and sea salt until smooth. Cool caramel completely, then divide among six heatproof ramekins and freeze for 15 minutes.
02 - Preheat oven to 425°F (220°C). Generously butter six 6-ounce ramekins and dust with cocoa powder or sugar, tapping out any excess.
03 - In a microwave-safe bowl or over a double boiler, melt chopped dark chocolate and unsalted butter together, stirring until the mixture is smooth. Allow to cool slightly.
04 - In a bowl, whisk eggs, egg yolks, and granulated sugar until the mixture is thick and pale. Stir in the melted chocolate-butter mixture, then gently fold in all-purpose flour and salt until just combined.
05 - Place frozen caramel portions into the bottom of each prepared ramekin. Divide the chocolate batter evenly over the caramel centers, ensuring the caramel is completely covered. Arrange ramekins on a baking sheet.
06 - Bake for 10 to 12 minutes until edges are set but centers are still soft and slightly jiggly. Allow to rest for 1 minute. Run a knife around the edges, invert each cake onto a plate, and remove the ramekins. Dust with powdered sugar, top with flaky sea salt, and serve immediately with vanilla ice cream.