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Preheat the oven to 450°F with a rack in the center. Generously butter two 4-ounce ramekins, making sure to cover every interior surface and the top rim, then sprinkle with granulated sugar, tapping out any excess. Spray the prepared ramekins with nonstick spray, then place on a baking sheet and set aside.
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In a medium microwave-safe bowl, heat the butter and chocolate in the microwave until completely smooth and melted, 30 to 45 seconds. If the chocolate doesn’t melt, return the bowl to the microwave and heat in 10-second increments, stirring between bursts.
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Separate the eggs: Place the whites in a medium bowl and set aside. Add the egg yolks to the bowl with the chocolate mixture, then whisk vigorously until fully incorporated and slightly thickened. Add the cocoa, vanilla, salt, and espresso powder and whisk until combined. (If the mixture looks separated, continue to whisk vigorously until it comes together and smooths out.)
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To the bowl with the whites, add the sugar. Whisk vigorously until the mixture is very frothy (no need to reach soft peaks), 1 full minute. Transfer the egg white mixture to the bowl with the chocolate mixture, then whisk until combined, with no streaks of white visible.
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Divide the batter evenly between the prepared ramekins (about 120g or a little over 1/2 cup batter in each); the ramekins will be very full — this is OK.
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Transfer the ramekins to the oven, still on the baking sheet, and bake for 8 to 10 minutes, until the cakes have risen about 1/2" over the rim of the ramekins and are just set on top, with no wet-looking spots. Be careful not to overbake.
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Remove the baking sheet from the oven and let it sit on a wire rack for about 2 minutes. In the meantime, if you notice any cake that looks stuck to the rim of the ramekin, gently loosen it with a small offset spatula.
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Place a plate over one ramekin, hold the ramekin with oven mitts, then carefully invert. Leave the ramekin upside down on the plate for about 10 seconds, then carefully remove it so that the cake unmolds onto the plate.
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Repeat with the second lava cake, then dust both generously with confectioners’ sugar. Serve immediately.