Preheat oven to 375°F. Grease and flour the bottom and all the way up the sides of an 8-inch cake pan. Use a parchment round or cut parchment to fit the bottom of the cake pan and then grease and flour that.
Place eggs in a small bowl and whisk to lightly beat them. This is just to break up the yolks so it’s easier to mix into the cake batter. Set aside.
We’re going to melt the chocolate over a double boiler. Fill a small or medium saucepan with 2-3 inches of water. Cover and bring to a boil over medium heat.
Break up the baking chocolate and add it to a large heat-safe bowl (be sure your bowl will fit on top of the pan that’s boiling on the stove). Add the butter with the chocolate and place the bowl on top of the pot of boiling water. Be careful not to burn yourself and not to get any water into the chocolate mixture.
Reduce heat to medium low and stir almost constantly until the chocolate and butter and smooth and melted.
Remove from the heat and stir in the sugar.
Stir the eggs into the chocolate mixture and stir until the eggs are completely mixed in.
Add the instant espresso and vanilla; stir.
Place the cocoa in a sifter and sift it onto the cake batter. Stir until completely mix. Pour cake batter into prepared pan.
Bake for about 25 minutes, or until the top looks solid. Mine took 25 minutes exactly at every test, but know that ovens all bake differently.
Cool 5 minutes, then run a butter knife around the edge carefully to loosen. Invert serving plate over the cake pan and carefully flip over to remove the cake from the pan (be careful not to burn yourself). Remove pan and parchment. Allow cake to cool completely.
Store covered at room temperature for up to 4 days.
Serving suggestions: dust with powdered sugar and/or cocoa, serve with raspberries or whipped cream.