Preheat your oven to 425°F (218°C). Thoroughly grease the bottoms and sides of four 6-ounce ceramic ramekins with softened butter using upward strokes. Dust the inside of each ramekin with unsweetened cocoa powder, tapping out any excess over the sink. Place ramekins onto a sturdy baking sheet.

Coarsely chop 6 ounces of bittersweet or dark chocolate. Place the chopped chocolate and 1/2 cup cubed unsalted butter in a heatproof glass bowl set over a saucepan of gently simmering water (or microwave in 25-second bursts at 50% power, stirring in between) until completely melted, silky smooth, and glossy. Whisk in pure vanilla extract and espresso powder. Set aside to cool slightly for 3 to 4 minutes.

In a separate medium mixing bowl, whisk together the 2 whole eggs, 2 egg yolks, 1/2 cup sifted powdered sugar, and 1/4 tsp fine sea salt until pale, slightly thickened, and ribbony (about 1 to 2 minutes by hand with a wire whisk).

Gently pour the warm melted chocolate-butter mixture into the whipped egg mixture. Whisk gently until fully incorporated and uniformly dark and luxurious.

Sprinkle the 3 tablespoons of all-purpose flour over the batter. Use a flexible silicone spatula to gently fold just until no dry flour streaks remain. Do not overmix to preserve the delicate, tender cake crumb.

Evenly divide the batter among the four prepared ramekins (each will be about 3/4 full).

Bake at 425°F (218°C) for precisely 12 to 14 minutes. Watch closely around minute 12: the outer edges should be firm, set, and puffed, while the very center circle (about the size of a quarter) remains slightly soft, glossy, and gently jiggles when nudged.

Remove from the oven and let the ramekins rest undisturbed on a cooling rack for exactly 2 minutes (no longer, or the residual heat will bake the molten center).

Run a thin knife gently around the top outer edge to ensure release. Carefully place an inverted dessert plate over the top of the ramekin. Using oven mitts, flip both plate and ramekin together. Let it sit inverted for 10 seconds, then gently lift the ramekin away—the warm cake should slide out cleanly.

Immediately dust with powdered sugar through a fine sieve, crown with a scoop of premium vanilla bean ice cream, and scatter fresh tart raspberries around the base. Pierce with a dessert spoon and watch the warm molten chocolate river pour out.