Preheat oven to 425 degrees F and adjust the oven rack to the upper-middle position. Grease four 4-ounce ramekins with butter, then coat with granulated sugar, tapping out the excess.
In a large bowl, whisk together the sugar and cornstarch.
In a medium heatproof bowl set over a pan of barely simmering water, melt the butter and chocolate together.
Add the chocolate mixture to the sugar mixture and whisk to combine. Add the eggs, egg yolks, and vanilla extract, and whisk until thoroughly combined.
Divide the batter between the prepared ramekins, place them on a rimmed baking sheet, and bake until the tops are set and look shiny on top, 13 to 16 minutes.
Remove from the oven, cool for 2 minutes, then run a paring knife around the edges of the ramekins. Carefully invert each cake onto a plate and serve immediately.
Chocolate: You can substitute semisweet chocolate if you prefer a sweeter dessert. However, DO NOT substitute chocolate chips for the chopped chocolate; chocolate chips have an emulsifier in them that helps them keep their shape, which inhibits their ability to totally melt into that “lava” or “molten” consistency.
Using a Muffin Tin: If you don’t have ramekins, you can divide the batter between 6 cups in a muffin tin. The bake time will be slightly shorter, so begin checking sooner. To remove them, carefully use a fork to lift them up, then invert onto plates.
Adding Liqueur: Feel free to add 1 teaspoon of liquor for an extra punch of flavor in place of the vanilla. Some ideas include Grand Marnier, brandy, or rum would be delicious.
Serving Suggestions: These cakes are fabulous on their own, or you can top them with fresh fruit, whipped cream, or ice cream (vanilla or coffee ice cream is awesome!).
Make-Ahead Instructions: The lava cakes can be prepared and the batter placed into the ramekins, then covered with plastic wrap and refrigerated for up to 24 hours. Remove the plastic wrap and bake as directed.
Freezing Instructions: Prepare as directed in the make-ahead instructions above. Cover with plastic wrap, then with foil, and freeze for up to 1 month. The cakes do not need to thaw; bake as directed from frozen, adding a minute or two to the baking time.