Preheat your oven to 350 degrees F. Line a 9x13-inch metal baking pan with parchment paper, or grease and flour the pan if using glass or ceramic. Set aside.

In a medium bowl, whisk together the cake flour, baking powder, baking soda, and salt. Set aside.

In a large bowl, using an electric mixer or stand mixer with the paddle attachment, beat the butter and sugar together until light and fluffy, about 2 minutes.

Gradually beat in the whole eggs and egg whites, one at a time, then mix in the vanilla extract and sour cream.

Add half of the flour mixture to the butter mixture and stir until just combined, then mix in the milk.

Add the remaining flour mixture and stir until just combined. Pour the batter into the prepared pan and spread evenly.

Bake for 25 to 30 minutes, or until a toothpick inserted into the center comes out clean. Let the cake cool completely in the pan on a wire rack before frosting.

In a large bowl, beat the butter, vanilla bean seeds, and salt together until light and fluffy, about 2 minutes.

Gradually add the powdered sugar, 1 cup at a time, beating well after each addition. Add the cream or milk, 1 tablespoon at a time, until the frosting reaches a spreadable consistency.

Beat on high speed for about 1 minute after the last addition of powdered sugar to make the frosting fluffy and airy. Spread the frosting evenly over the cooled cake and decorate with sprinkles if desired.