Position a rack in the center of the oven and preheat it to 350 degrees F. Line a baking sheet with a silicone baking mat.
Place the chocolate and butter in a double boiler (or a medium heatproof bowl over a medium saucepan of barely simmering water--do not let the bowl touch the water) and heat over low heat, stirring often, until melted, about 3 to 5 minutes. Set aside but keep warm.
Combine the eggs, sugar and vanilla in the bowl of a stand mixer fitted with the paddle attachment. Beat together starting on low speed and slowly increasing the speed to medium, until light and creamy, 3 to 4 minutes.
Combine the flour, espresso powder, baking powder and fine sea salt in a small bowl. Whisk to combine.
With the mixer running on low speed, gradually add the flour mixture to the beaten eggs and mix for 1 minute. Scrape down the sides. With the mixer running on low speed, pour in the melted chocolate. Stir until everything is fully incorporated without overworking the batter, 30 to 45 seconds.
Let the dough sit for 5 minutes to firm up.
Using a 1-tablespoon portion scoop, scoop 6 to 8 mounds of the dough and place on the prepared baking sheet, spacing them 1 inch apart. If the dough spreads out, it needs more time to firm up. Sprinkle the tops with fleur de sel.
Bake on the center rack until the tops of the cookies look cracked and shiny, 8 to 10 minutes.
Let the cookies cool on the baking sheet for 1 minute to set up, if necessary, then transfer the cookies to a wire rack and let cool completely.
Repeat the scooping and baking with the remaining dough.