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Preheat the oven to 350 degrees. Spray a 9-inch square baking dish with cooking spray and set aside.
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Combine the chocolate and butter in a microwave-safe bowl and heat in 30-second intervals, stirring after each interval, until chocolate is melted and mixture is smooth. Let cool for 5 minutes.
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Combine the eggs and sugar in a large mixing bowl. Beat with an electric mixer set to medium-high for several minutes, until very thick. Add the vanilla, espresso powder, and salt and beat to combine.
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Gradually beat in the chocolate-butter mixture until fully incorporated. Beat in the cocoa powder until combined.
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Pour the batter into the prepared pan and smooth the top. Bake for 30 to 35 minutes, until the center just barely jiggles if you tap the side of the pan.
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Set pan on a wire rack and cool completely before slicing and serving.