Preheat oven to 350°F. Lightly coat an 8x8-inch square baking pan with nonstick spray or line with parchment paper and set aside.
In a small bowl, whisk together egg, egg white, yogurt, and vanilla until smooth.
In a saucepan, combine sugar, oil, water, and salt. Set over medium heat and warm, stirring constantly to prevent sugar from sticking, until sugar is warmed but not completely dissolved.
Remove from heat and add the chocolate and cocoa. Stir until completely melted, then stir in egg mixture until smooth. Add the flour and stir just until it is incorporated.
Pour the batter into the prepared pan, spreading to the edges. Bake for 25 minutes. Cool completely in the pan before serving.