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In a large bowl, beat butter until light and fluffy. Add in brown sugar and white sugar; beat until light and fluffy.
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Add in egg, beating well. Add in vanilla and salt. Mix.
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In a separate bowl, sift together flour, cocoa powder, baking soda, corn starch, and espresso powder. Gently incorporate dry ingredients into the wet ingredients, stirring until just combined.
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Chill dough in fridge for 30-60 minutes.
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Preheat oven to 350 degrees and spray a 24-cup mini muffin tin with baking spray.
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Press 1 Tbsp of dough into each cup, forming dough into the shape of a cup.
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Bake for 12-13 minutes, or until dough has baked up into a cookie shell. Because the dough will have expanded, while the cookie cups are cooling in the pan, take a 1 Tbsp measuring spoon and press it into the center of each cookie to reinforce the cup shape.