Begin by preparing the lava centers, which need time to set before baking. Chop 4 ounces of dark semi-sweet chocolate into pieces and place in a metal bowl. Heat 3 ounces of heavy cream and pour it over the chocolate, then whisk until smooth.
Add 2 teaspoons of butter and whisk until fully incorporated. Transfer the mixture to the refrigerator and whisk periodically until it reaches a frosting-like consistency. Once ready, use a spoon or melon-baller to form cherry-sized mounds on a cookie sheet and freeze until needed. This step can be completed several hours or even a day in advance, making it convenient for advance preparation.
For the cake batter, chop 14 ounces of dark semi-sweet chocolate into pieces and place it on top of a double boiler with 8 ounces of butter to melt together. Remove from heat and add 2 teaspoons of vanilla extract and 3 egg yolks, whisking until the mixture is smooth.
Gently fold in 3 ounces of sifted cake flour until fully incorporated. In a separate clean bowl, combine 3 egg whites with 1/4 teaspoon of cream of tartar and whisk until soft peaks form. Slowly sprinkle in 4 ounces of sugar while continuing to whisk. Using a rubber spatula, carefully fold the egg white mixture into the chocolate mixture in three additions, being gentle to maintain the airiness.
Spoon the batter into large non-stick muffin tins, filling each 3/4 full (alternatively, use buttered and cocoa-dusted ramekins). Insert a frozen lava center into the middle of each cake and bake at 375°F for exactly 15 minutes—do not overbake, as this will compromise the molten center. Remove from the oven, wait 5 minutes, then carefully unmold each cake onto a wire rack. Serve the cakes warm, or reheat in the microwave for 30 seconds if necessary.