In the bowl of an electric mixer beat the eggs and the sugar for 4 to 6 minutes, or until the mixture is thick and pale, add melted chocolate, the butter, the vanilla, the espresso, the flour, the salt and the baking powder, and beat the mixture on the lowest setting until it is combined well.
In a sheet of parchment paper, form the dough into a log, 4 inches in diameter, wrap it in wax paper, and chill it for 3 hours, or until it is firm.
Cut the log into 1-inch-thick rounds, arrange the rounds 2 inches apart on baking sheets lined with parchment paper, and bake them in batches in the middle of a preheated 350°F oven for 15 minutes, or until the tops are shiny and cracked slightly.
The cookies will be very soft
Transfer the baking sheets to racks and let the cookies cool completely before removing them from the sheets.