Begin by preheating your oven to 425°F (220°C). Generously grease four ramekins with butter or non-stick spray, then lightly dust with cocoa powder to prevent sticking. Set aside while you prepare the batter.
In a double boiler or microwave-safe bowl, melt the unsalted butter and semi-sweet chocolate chips together. Stir gently until smooth and glossy, then remove from heat and let cool slightly.
In a medium bowl, whisk together the whole eggs, egg yolks, and granulated sugar until the mixture is pale, slightly thickened, and fluffy. This aeration helps create a tender crumb.
Slowly pour the melted chocolate mixture into the egg mixture, whisking continuously to incorporate. Add the brewed espresso, vanilla extract, and a pinch of salt, mixing well. Gently fold in the all-purpose flour until just combined—be careful not to overmix.
Divide the batter evenly among the prepared ramekins. Place them on a baking sheet and bake for 12-14 minutes. The edges should be firm but the centers still soft and slightly jiggly when you gently shake the ramekin.
Allow the cakes to cool for 1-2 minutes before carefully inverting them onto serving plates. The lava center will ooze out as you cut into them. Serve immediately for the best molten experience.