Preheat oven to 350°F. Lightly coat a 9-inch springform pan with nonstick cooking spray; set aside. In a medium saucepan, stir together sugar, the water, and espresso powder. Cook and stir over medium-low heat until the sugar dissolves and mixture almost boils. Stir in the chocolate until melted. Remove from heat. Place egg yolks in a small bowl. Gradually stir the chocolate mixture into egg yolks; stir in vanilla (mixture may appear slightly grainy). Set aside.
In a medium bowl, stir together the cocoa powder, flour, and baking powder. Stir in chocolate-egg yolk mixture until smooth. In a large bowl, beat egg whites with an electric mixer on medium speed until stiff peaks form (tips stand straight). Stir a small amount of the beaten egg whites into the chocolate mixture to lighten. Fold chocolate mixture into remaining egg whites. Spread in the prepared pan.
Bake about 30 minutes or until the top springs back when lightly touched. Cool in pan on a wire rack for 10 minutes. Loosen and remove side of pan. Cool completely. (Cake may fall slightly but evenly during cooling.)
To serve, cut cake into wedges. If desired, sprinkle dessert plates with additional cocoa powder. Transfer wedges of cake to dessert plates. Top with whipped topping and berries.