- Preheat oven to 350°F. Grease 13- x 9-inch pan; line with parchment paper.
- In small bowl, whisk together flour, baking powder, baking soda and salt.
- In large bowl, whisk sugar with oil. Whisk in egg white and egg; whisk in 1 tbsp vanilla.
- In measuring cup, combine buttermilk and strawberry purée; stir into egg mixture alternately with flour mixture, making three additions of flour mixture and 2 of buttermilk mixture. Pour into prepared pan.
- Bake for 30 to 40 minutes or until toothpick inserted into center comes out clean. Let cool completely on rack.
- Icing: In heatproof bowl, whisk together sugar and egg whites; set over pan of simmering water (ensuring bowl does not touch water). Whisk until sugar is dissolved and mixture is warm to the touch. Transfer to electric stand mixer fitted with whisk attachment; beat on high speed until fluffy, voluminous and cooled. Reduce speed to medium; beat in butter, 1 tbsp at a time. Increase speed to high; beat until silky. Reduce speed to medium-low; beat in freeze-dried strawberry powder and vanilla.
- Spread buttercream evenly over cake. Arrange strawberries and blueberries in striped pattern over top to resemble flag.
Tip: If freeze-dried strawberry powder is not available, substitute 1/3 cup strawberry purée in the buttercream.