Preheat oven to 350°.
Fit dough into a 9-inch pie plate. Fold edges under; flute. Place pie plate in freezer until ready to use.
Combine brown sugar, 1/2 cup cocoa, and flour in a large bowl. Combine milk and next 5 ingredients (milk through egg whites); stir with a whisk until well blended. Add milk mixture to brown sugar mixture; stir until combined.
Pour mixture into crust. Bake at 350° for 40 minutes or until just set. Cool on a wire rack to room temperature. Cover; chill at least 4 hours. Spread whipped topping evenly over filling; sprinkle with 1/2 teaspoon cocoa, if desired.