Adjust oven rack to middle position and preheat oven to 350°F (175ºC). Using baking spray, coat the interior of a 9-inch springform pan; line bottom of pan with a parchment paper round and the sides with a separate parchment strip; set aside.

Fill a medium saucepan with water to a depth of 1 inch and bring to a boil over medium-high; reduce heat to a simmer over medium-low. In a medium-size heatproof bowl, combine chocolate, butter, espresso powder, and salt, and place over saucepan of simmering water. Cook, stirring frequently, until chocolate mixture is melted and smooth, 5 to 6 minutes. Remove from heat, being careful not to drip any water into the melted chocolate. Whisk in cocoa powder and vanilla extract until combined and smooth; set aside.

In the bowl of a stand mixer fitted with the whisk attachment, combine eggs and sugar. Whisk on medium-high speed until mixture is pale, falls off the whisk attachment in thick ribbons (they should slowly sink back into the batter) and has increased by about ⅓ in volume, 5 to 7 minutes. (Alternatively, an electric hand mixer fitted with the whisk attachment can be used to whip the eggs and sugar.) Using a flexible spatula, fold chocolate mixture into eggs gradually until just combined and no streaks remain. Gently scrape chocolate batter into prepared pan, using a small offset spatula to evenly spread and smooth the top if necessary.

Bake until top is dry and a wooden toothpick inserted near center of cake comes out with a few moist crumbs, about 25 minutes. Let cool in pan on a wire rack for 30 minutes. Run a small offset spatula or butter knife around edges of cake to loosen, if necessary; remove pan sides, and discard strips of parchment. Let cake cool completely on pan base on wire rack, about 1 ½ hours. Using a large offset spatula, gently loosen cake from pan base and carefully transfer cake to a plate, removing and discarding parchment round. Using a fine-mesh sieve, dust cake with additional cocoa powder. Serve with sweetened whipped cream or vanilla ice cream, if desired.