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Preheat the oven to 350 degrees, and line two baking sheets with parchment paper or a non-stick sheet.
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In a medium bowl, whisk together the flour, cocoa powder, baking soda, baking powder, salt, and espresso powder. Set aside.
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In a large bowl, beat together the melted butter, brown sugar, and 3/4 cup sugar.
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Mix in the vanilla extract, egg, egg yolk, and coffee.
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Slowly add in the flour mixture, and stir until completely combined.
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Scoop rounded tablespoonfuls of the dough into your hands, and roll into a ball. In a small bowl, mix the 1/2 cup sugar and 1 tsp. espresso powder. Roll each dough ball in the sugar mixture to coat.
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Place on your baking sheet, and press down each dough ball slightly with the bottom of a glass.
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Bake for 8-10 minutes, or until the cookies are set and have cracks on the edges and top.