In a large bowl, beat butter until light and fluffy. Add in brown sugar and white sugar; beat until light and fluffy.
Add in egg, beating well. Add in vanilla and salt. Mix.
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.
Chill dough in fridge for 30-60 minutes.
Preheat oven to 350 degrees and spray a 24-cup mini muffin tin with baking spray.
Press 1 Tbsp of dough into each cup, forming dough into the shape of a cup.
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.