Make the cake

• Preheat the oven to 350°F with a rack in the center position. Grease a sheet pan with nonstick spray.
• In a large bowl, vigorously whisk together the eggs and granulated sugar for 1 minute, until well combined and very frothy. Whisk in the melted butter, oil, buttermilk, vanilla, and almond extract until smooth.
• Add the flour, baking soda, baking powder, and salt. Gently fold with the whisk until the batter is smooth and streak-free.
• Pour the batter into the prepared pan and spread it evenly to the corners with a large offset spatula. Bake for 18 to 20 minutes, until the cake is golden and pulls away from the sides of the pan and a tester inserted into the center comes out clean. Run a paring knife around the edges of the cake to loosen and then allow the cake to cool completely in the pan, about 25 minutes.
• Meanwhile, make the frosting: In the bowl of a stand mixer fitted with the whisk attachment or in a large bowl with a handheld mixer, whip together the cream, yogurt, and sugar until medium-stiff peaks form, about 3 minutes. Add the lemon zest and vanilla and whisk until stiff peaks form, about 2 minutes more.
• Spread the frosting in a thick, even layer over the cake. Use a toothpick or small offset spatula to faintly outline the shape of the American flag in the frosting to guide you as you decorate. Arrange the blueberries in the upper left corner as the “stars,” and make red stripes by arranging double rows of raspberries and/or overlapping strawberry slices over the rest of the cake.
• Chill the cake in the refrigerator, uncovered, until ready to serve. The cake will keep, tightly covered, in the refrigerator for up to 3 days.