Place a medium-sized heat-safe bowl over a medium saucepan with 3 to 4-inches of simmering water on low heat. You can also use a double boiler. Add chocolate, butter, and espresso powder to the bowl.
Stir the chocolate mixture constantly until smooth and melted.
Remove chocolate from heat, and add ¾ cup granulated sugar and all of the brown sugar. Mix until smooth.
Whisk in the eggs and vanilla, set aside.
In a medium bowl, whisk together flour, cocoa powder, baking powder, baking soda, and salt.
Fold the dry ingredients into the wet ingredients until just combined.
Cover the bowl with plastic and let the dough chill in the refrigerator for 20 to 30 minutes.
Preheat the oven to 350°F and line a baking sheet with parchment paper.
Place the remaining granulated sugar in a small bowl.
Use a medium cookie scoop to portion the dough and roll carefully to create a ball.
Roll the dough balls into the remaining granulated sugar until coated.
Place the cookies 1 to 2-inches apart on a baking sheet. Bake for 9 to 11 minutes. The cookies will appear underdone when removed from the oven, this is what you want.
Allow cookies to cool for 15 minutes on the baking sheet before transferring to a cooling rack.