Makes one 9-inch cake
1. Preheat the oven to 300°F. Lightly grease a 9-inch round cake pan. Cut a circle of parchment paper to fit the bottom of the pan, and press it into place.
2. In a small saucepan over high heat, bring the sugar and water to a boil, stirring to dissolve the sugar. Turn off the heat and add the chocolate, stirring with a wooden spoon until fully melted.
3. Add the butter and vanilla to the chocolate mixture and stir until the butter is melted. Let the mixture cool completely.
4. Using an electric mixer fitted with the paddle or beater attachment, beat the eggs on high speed until they are lighter in color and creamy, 3 to 4 minutes.
5. Reduce the mixer speed to low and slowly add the chocolate mixture, mixing just until the chocolate is fully incorporated, about 30 seconds. Pour the cake batter into the prepared cake pan.
6. Bake the cake until the sides of the cake look firm and set, but the center still appears slightly wet, about 1 hour.
7. Remove from the oven and let cool completely before removing from the pan. Dust with confectioners’ sugar and serve.