6 tablespoons (3/4 stick) cold unsalted butter cubed, plus more, room temperature, for ramekins
1/3 cup sugar plus more for ramekins
6 ounces bittersweet chocolate chopped
2 large eggs plus 2 large egg yolks
1/4 cup all-purpose flour (spooned and leveled)
1/2 teaspoon coarse salt
caramel Sauce for serving
whipped cream for serving
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.
Caramel Sauce: In a medium saucepan, heat 1 cup 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 6 tablespoons (3/4 stick) cold unsalted butter, cubed, 1/2 teaspoon coarse salt, and 1/2 teaspoon pure vanilla extract (take care as mixture is extremely hot and will bubble).
Whisk in 1/2 cup heavy cream.
Pour into a heatproof container and let cool. (To store, refrigerate, up to 3 weeks.)