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Preheat the oven to 375°F. Lightly grease a metal 8" round cake pan; cut a piece of parchment to fit, grease it, and lay it in the bottom of the pan. See "tips," below.
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To make the cake: Put the chocolate and butter in a microwave-safe bowl, and heat until the butter is melted and the chips are soft. Stir until the chips melt, reheating briefly if necessary. You can also do this over a burner set at very low heat. Transfer the melted chocolate/butter to a mixing bowl.
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Stir in the sugar, salt, espresso powder, and vanilla. Espresso enhances chocolate's flavor much as vanilla does; using 1 teaspoon will simply enhance the flavor, while 2 teaspoons will lend a hint of mocha to the cake.
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Add the eggs, beating briefly until smooth. Add the cocoa powder, and mix just to combine.
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Spoon the batter into the prepared pan.
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Bake the cake for 25 minutes; the top will have formed a thin crust, and it should register at least 200°F on an instant-read thermometer inserted into its center.
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Remove it from the oven, and cool it in the pan for 5 minutes.
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Loosen the edges of the pan with a table knife or nylon spreader, and turn it out onto a serving plate. The top will now be on the bottom; that's fine. Also, the edges will crumble a bit, which is also fine. Allow the cake to cool completely before glazing.
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To make the glaze: Place the chocolate in a heatproof bowl. Heat the cream until it's not quite at a simmer, but showing fine bubbles around the edge. Pour the cream over the chocolate, stir very briefly to combine, and let rest for 5 minutes. Stir again — at first slowly, then more vigorously — until the chocolate is completely melted and the glaze is smooth. If any bits of chocolate remain, reheat briefly in the microwave or over a burner, then stir until smooth.
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Spoon the glaze over the cake, spreading it to drip over the sides a bit. Allow the glaze to set for several hours before serving the cake.
