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Preheat oven to 350°F/175°C. Lightly greases an 8-inch springform pan and line with a parchment round; oil parchment.
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Melt coconut oil and chocolate, in the microwave in 30-second intervals stirring in between, until the chocolate is completely melted and has a smooth consistency.
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Whisk together egg yolks and 1/2 cup sugar with a mixer on medium-high speed until thick and pale, about 3 minutes. Add espresso powder and salt; beat until combined, about 1 minute. Add vanilla and melted chocolate mixture; beat about 1 minute more.
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In another bowl, whisk egg whites on medium-high speed until foamy. Increase speed to high; gradually add remaining 1/2 cup sugar, beating until stiff peaks form, about 5 minutes. Fold into chocolate mixture in 3 batches. Transfer batter to pan and bake until set, 40 to 45 minutes. Let cake cool completely in pan on a wire rack. Remove side of pan; transfer cake to a serving plate.