Preheat your oven to 350°F (175°C). Lightly spray a rimmed 18x13x1-inch half-sheet baking pan with non-stick cooking spray, dust it with a thin layer of flour, and shake out any excess. In a medium bowl, thoroughly whisk together the flour, cornstarch, baking powder, baking soda, and salt for 30 seconds. Set aside.

In a large bowl, use an electric hand mixer on low to blend the sugar, 10 tbsp of softened butter, and 2 tbsp of the oil. Increase the speed to high and whip for 2–3 minutes until light and fluffy. Slowly blend in the remaining oil. On low speed, mix in the eggs one at a time, followed by 1 tbsp of vanilla extract, mixing just until combined to prevent a spongy texture.

Add 1/3 of your flour mixture to the wet batter and blend on low until barely mixed. Pour in half of the buttermilk, blending gently. Repeat with another 1/3 of the flour, the remaining buttermilk, and finish with the last of the flour. Use a rubber spatula to give the batter a final, gentle fold from the bottom to ensure everything is combined without overmixing.

Pour the batter into your prepared sheet pan and spread it evenly into the corners. Wiggle the pan gently to level the surface. Bake in the center of the oven for 25–30 minutes until a toothpick inserted into the center comes out clean or with a few moist crumbs. Remove from the oven and let it cool completely on a wire rack for 1.5 to 2 hours.

In a clean bowl, beat 12 tbsp of softened butter and the cream cheese together on medium-low speed for 1 minute until smooth. Add 1 tsp of vanilla and the powdered sugar, blending on low until incorporated. Raise the speed to high and whip for 3–5 minutes until light and fluffy. Spread the frosting evenly over the cooled cake with an offset spatula, then chill the cake briefly while preparing the fruit.

Shortly before serving, arrange a solid rectangle of blueberries in the upper-left corner (about 1/3 of that section) to represent the stars. Moving across the long width of the pan, arrange 4 parallel rows of sliced strawberries alternating with 3 parallel rows of whole raspberries to create the red and white flag stripes.