Preheat oven to 425ºF. Heavily butter and then flour 8 (1-cup) ramekins or coffee cups. Set cups on a cookie sheet. Chop chocolate into small even pieces. Melt with the butter in a double boiler over barely simmering water (or microwave, uncovered, on MEDIUM, stirring every 20 to 30 seconds after the first one or two minutes, until only a small chunk of solid chocolate remains). Remove from heat and stir until melted, smoother and cooled.
Beat eggs, yolks and sugar together at high speed for 6 to 8 minutes. The mixture will become thick like cream and become beige-colored. Fold in the cooled chocolate and vanilla extract. Sift the flour over chocolate and fold in . Pour batter into prepared cups. Bake 7 minutes. Pull out of oven and tuck a piece of frozen lava deep into the center of the half-baked batter in each cup. Return to oven and bake for 6 to 7 minutes more. Cakes will rise straight over the rims of the cups and may crack slightly. Cool in cups on a wire rack for 10 minutes.
Chop chocolate evenly. In a saucepan, heat half the cream with sugar until it boils. Remove from heat. Add chocolate and stir until it melts and sauce is smooth. Add remaining cream and stir again, patiently, until thick and smooth. Warm sauce gently for pouring. If allowed to set at room temperature, it will turn the consistency of sour cream and can be used like frosting. Makes 2 cups.
To assemble, make Chocolate Sauce. Drizzle Chocolate Sauce in a north-south zigzag over the caramel. Pull a wooden pick or knife back and forth cross the chocolate, going east-west to create a feathering effect. Run a thin knife around each cake to carefully loosen, then invert onto the sauce. Top with warm Chocolate Sauce, letting sauce drip down the sides of the cakes. If desired, decorate with fresh berries. Serve warm. When cut, chocolate will spill out of the warm cake.