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Preheat the oven to 325ºF. Line an 8-x-8-inch square baking pan with foil so that it extends up the sides. Spray the foil with nonstick spray.
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To make the oatmeal base and topping, combine the oats, sugar, flour, baking powder, baking soda, and salt in a medium bowl. Add the melted butter and stir to combine. Reserve 3/4 cup of the mixture for the topping. Press the remaining mixture into an even layer in the prepared pan. Bake until golden-brown, about 12 minutes.
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To make the fudge later, combine the flour, sugar, espresso powder, and salt in a medium bowl.
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Melt the chocolate chips and remaining 2 tablespoons of butter in the microwave, stirring every 30 seconds until smooth. Let cool slightly. Whisk in the egg, then fold in the flour mixture.
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Pour the chocolate mixture into the pan over the cooled crust and spread in an even layer. Sprinkle with the reserved oatmeal mixture. Return to the oven and bake until set and the topping is golden-brown, 25 to 30 minutes. Cool completely. Using the foil as handles, lift out of the pan and cut into bars.