Preheat the oven to 350°F. Butter and flour an 18 x 13 by 1 1/2-inch sheet pan.: As the oven warms you will notice a dry heat that promises lift and browning. Greasing and flouring the pan prevents the cake from sticking; run your finger along the sides to check for even coating. A common mistake is skipping the flour after buttering which can cause the cake to cling to the pan's surface. If you see uneven shine on the pan, add a touch more flour and tap out the excess so the cake releases cleanly after cooling.
In a large bowl, use an electric mixer to cream the butter and sugar on high speed, until light and fluffy. On medium speed, add the eggs, 2 at a time, then add the sour cream and vanilla. Scrape down the sides and stir until smooth.: While creaming you should hear a steady whir and see the mixture transform from grainy to paler and airy; this aeration is what gives the cake lift. When adding the eggs , the batter will momentarily look broken, but it should emulsify again with continued mixing. If the batter looks curdled or watery, you probably added cold eggs ; let ingredients come to room temperature next time. Scrape the bowl well so pockets of unincorporated butter do not remain, otherwise you risk dense spots in the cake.
In a medium bowl, sift together the flour, cornstarch, salt, and baking soda. Blend the flour mixture into the butter mixture until just combined. Pour into the prepared pan. Smooth the top with a spatula. Bake in the center of the oven for 20 to 30 minutes, until a toothpick comes out clean. Cool to room temperature.: The dry ingredients will smell faintly of grain and give a fine, dusty texture when sifted. When you fold them into the wet mix, stop as soon as you no longer see streaks of flour; over mixing activates gluten and makes the cake tough. After pouring, smooth gently so the surface is even; this helps the frosting sit flat. While baking, the kitchen fills with a warm vanilla aroma and the top should become lightly golden. A common error is opening the oven too soon which can cause the cake to sink in the middle; wait until the final minutes before testing with a toothpick. Letting the cake cool fully prevents the frosting from melting into the crumb.
In a large bowl, use an electric mixer to combine the butter, cream cheese, sugar, and vanilla, mixing just until smooth.: As you beat, the frosting should look glossy and feel silky, with no visible specks of cream cheese . Keep the speed moderate to avoid incorporating too much air which can make piping unstable. If the frosting looks grainy, sift the powdered sugar again and beat at low speed until smooth. A frequent pitfall is using chilled cream cheese , which leaves lumps; ensure it's fully softened for an even, spreadable finish.
Spread three-fourths of the frosting on the top of the cooled sheet cake. Outline the flag on the top of the cake with a toothpick. Fill the upper left corner with blueberries. Place 2 rows of strawberries across the top of the cake like a red stripe. Put the remaining frosting in a pastry bag fitted with a star tip and pipe two rows of white stripes below the strawberries. Alternate rows of strawberries and frosting until the flag is completed. Pipe stars on top of the blueberries.: The moment you spread frosting you will feel a creamy resistance under the spatula, and the cake should not crumble as you smooth it. Use a toothpick to mark the flag proportions so the layout stays balanced. Press the blueberries gently into the frosting so they anchor without releasing excess juice. When arranging strawberries , align slices for clean red lines, and pipe the white stripes with steady pressure to create crisp ridges. A typical mistake is overpressing fruit into the frosting which squeezes juice and softens the pattern, so handle fruit with a light touch and wipe any run off immediately.