Preparation

1. Preheat the oven to 350°F with the rack in the middle position. Spray a 13x9-inch cake pan with nonstick cooking spray and then line the bottom with parchment paper. Reserve.
2. Put the flour, sugar, baking powder, and salt into a large mixing bowl. Using the beaters, mix on Speed 1 to fully combine, at least 30 seconds. Reserve.
3. Put the buttermilk, eggs, yolks, and vanilla extract into a medium bowl. Mix on Speed 3 until combined.
4. Reduce to Speed 2. Gradually add the oil to the dry ingredients, and mix until combined. Increase to Speeds 4 to 5 and mix until smooth, about 1½ minutes.
5. Gradually add the liquid mixture, mixing on Speed 2 until completely combined.
6. Pour the batter evenly into the prepared cake pan. Tap gently on the countertop to remove any bubbles, and then place in the oven. Bake until the center springs back to the touch and a cake tester comes out clean when inserted in the center, about 25 minutes.
7. Remove from the oven. Transfer the pan to a wire cooling rack to cool completely before topping.
8. While the cake is cooling, prepare the whipped cream. Put the heavy cream, confectioners’ sugar, vanilla, and salt in a large bowl. Insert the whisk attachment. Select Speed 1 and whisk to combine. Gradually increase to Speed 9 until the cream reaches desired stiffness. Whipped cream will reach soft peaks between 50 and 60 seconds.
9. Once the cake is cool, remove from the pan and transfer to a serving platter or board. Spread the whipped cream over the top of the cake. Using the blueberries, fill the top left corner in a neat manner to make a square (to represent the stars). Using the raspberries, create 7 stripes across the cake, leaving even space between the berries to make 6 white stripes. 
10. Serve immediately. Note: This cake can be prepared ahead. Bake the cake 1 day before you plan to serve it, and then cool and wrap well. Top with the whipped cream and berries just prior to serving.