Melt 8 ounces of chocolate, the butter, and espresso powder in the top of a double boiler placed over simmering water, stirring until smooth and melted. Remove from the heat and let cool slightly.
Whisk together the flour, baking powder, and salt in a small bowl to combine.
Whisk together the eggs, sugar, and vanilla extract in a medium bowl to combine. Add the melted chocolate mixture and whisk until fully incorporated. Fold in the flour mixture and remaining 2 ounces of chocolate and mix until just combined. Cover the dough with plastic wrap and chill in the refrigerator for at least 1 hour, or overnight.
Preheat the oven to 325°F and line a few baking sheets with parchment paper. Using a small ice cream scoop, drop the dough onto the baking sheets, spacing the cookies 1-inch apart. Bake for about 10 minutes, until the tops are dry and cracked. Remove from the oven and top each cookie with a pinch of sea salt. Let cool for 5 minutes, then transfer the cookies to a wire rack and let cool completely.