Preheat oven to 350 degrees. Butter four 6-ounce ramekins, then coat lightly with sugar, tapping out excess. In a microwave-safe bowl, combine butter and chocolate. Microwave until melted, about 1 minute; stir until smooth. (Or melt mixture in a heatproof bowl set over, not in, a pan of simmering water.)
In a large bowl, whisk together sugar, eggs, yolks, flour, and salt; add chocolate mixture and whisk to combine. Fill each ramekin three-quarters full with batter; place on a rimmed baking sheet and refrigerate 15 minutes.
Bake until center of a cake is soft but not wet when pressed, 27 to 30 minutes. Let cool 5 minutes. Serve cakes warm, topped with caramel and whipped cream.
In a medium saucepan, heat 1 cup over medium-high until melted and brown at edges, 3 minutes. With a heat-resistant spatula, pull melted sugar toward center until all sugar is melted and caramel is deep amber in color, 3 minutes more.
For the best texture, don't overbake them. Lightly coating the ramekins with sugar helps the cakes rise as they bake and makes them easy to unmold before serving, if you like.
In a medium saucepan, heat sugar over medium-high until melted and brown at edges, 3 minutes. With a heat-resistant spatula, pull melted sugar toward center until all sugar is melted and caramel is deep amber in color, 3 minutes more.
Immediately whisk in butter, coarse salt, and pure vanilla extract (take care as mixture is extremely hot and will bubble).
Whisk in heavy cream.
Pour into a heatproof container and let cool. (To store, refrigerate, up to 3 weeks.)