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Bring the oven temperature up to 350 degrees Fahrenheit. Apply butter to the base and edges of a metal baking pan that measures 9×13 inches. Line the bottom of the pan with a lengthy piece of parchment paper, ensuring that it extends up two sides and slightly overhangs on both ends. Repeat with a second layer of parchment paper, this time positioning it perpendicular to the first. (Once cooked, the bars will be easier to remove from the pan if you do this.) Grease the baking sheet.
Combine the espresso powder, cocoa, and hot water in a large bowl and whisk until smooth. While whisking, add the unsweetened chocolate and melt it. Stir in the oil and melted butter. When the mixture is completely combined, whisk in the eggs, yolks, and vanilla. Add sugar and whisk until combined. Combine the flour and salt by using a rubber spatula to stir them together.
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