Preheat the oven to 350°F and line a 13"x9" sheet pan with parchment paper. Sift together the cake flour, baking powder, kosher salt, and granulated sugar, whisk to combine, and set aside. In a separate bowl, whisk the egg whites with the milk, vanilla extract, and sour cream until smooth. Fit a stand mixer with a paddle attachment and cream the room-temperature butter until soft. Gradually beat in the dry ingredients until a crumb-like texture forms. Pour in half of the wet mixture, blend, scrape down the sides, then add the remaining liquid and beat until just incorporated. Halve the raspberries, drizzle them with lemon juice, sprinkle with a pinch of flour, and toss gently. Fold both the raspberries and blueberries into the batter by hand. Spread the batter evenly into the prepared pan, then scatter a few extra berries on top. Bake for 35–40 minutes or until a toothpick inserted into the center emerges clean. Allow the cake to cool completely on a wire rack.

In the stand mixer fitted with a whisk, whip the cold heavy cream and confectioners sugar on high speed until stiff peaks form. Add the vanilla extract and whip briefly. Gently fold in the mascarpone cheese by hand with a spatula, then whisk until smooth and fluffy.

Once the cake is cool, trim the edges if desired for a clean finish. Use an ice cream scoop to dollop the frosting on top, then smooth it evenly with an offset spatula. Sketch the flag design lightly using a ruler for precision, then arrange blueberries in the upper left corner and lay raspberries in rows to complete the flag pattern.