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Preheat oven to 325°F and set aside a greased 8-inch square baking pan or 9-inch round baking pan.
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In a large bowl, whisk together all-purpose flour, sugar, cocoa powder, baking soda, baking powder, and salt. Set aside.
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In a separate bowl, whisk together coffee, oil, milk, vanilla, and egg.
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Add liquid ingredients to flour mixture, and whisk until thoroughly combined. Transfer batter to prepared baking pan and bake until an inserted toothpick near the center comes out clean, about 30 to 40 minutes. Cool in the pan for 15 minutes, then transfer to a wire rack to cool completely.