1. Preheat oven to 350°F. Butter a 9-inch springform pan and line bottom with parchment. Butter parchment.
2. Combine chocolate, sugar and espresso powder in bowl of a food processor. Process until chocolate is finely ground, about 30 seconds. With blades in motion, pour in 3/4 cup boiling water. Process until chocolate has melted, about 20 seconds. Add butter, eggs and vanilla. Pulse several times to thoroughly mix into a thin batter.
3. Pour batter into springform and swirl to evenly spread batter. Bake until set in center, 55 to 60 minutes (cake will appear dry on top and slightly cracked around the edges). Let cool in pan on a wire rack for 20 minutes; cake may sink in center. Run a thin knife around edges of pan, remove cake from pan, cover and refrigerate until well chilled, at least 2 hours or overnight.
4. Place cake on a serving plate and let stand at room temperature for 15 to 30 minutes. Just before serving, sift confectioners' sugar over cake. Serve with whipped cream, if desired.