Preheat the oven to 325°F. Generously butter an 8 or 9-inch springform pan, and line the bottom with parchment paper. Butter and flour the paper; set aside.
In a heavy saucepan over medium heat, melt the butter; add the sugar and espresso and stir until the sugar dissolves. Add the chocolate and stir until smooth. Remove the pan from heat and set aside to cool slightly. You don't want it to be hot when you add the eggs.
Whisk the whole eggs and egg yolks in a large bowl until frothy. Quickly whisk the eggs into the chocolate mixture. Pour the batter into the prepared pan and place the pan on a baking sheet.
Bake until the edges puff and crack slightly but the center is not completely set, about 1 hour; don't over bake (the cake will continue to set as it cools). Transfer to a rack and cool. Cover and refrigerate overnight for best results.
When ready to serve, run a small knife around the cake pan to loosen. Carefully release the pan sides. Sift powdered sugar over the cake. Cut into small wedges, wiping the knife clean before each cut. Serve with ice cream or whipped cream.
Notes
If you are preparing this recipe as gluten-free, just be sure to use a brand of chocolate that is known to be GF.