Preheat the oven to 350F degrees. Line a 9×13" metal baking pan with parchment paper or grease and flour if using a glass or ceramic baking dish. Set aside.
In a medium-sized bowl whisk together the flour, baking powder, baking soda, and salt. Set aside.
Slowly beat in the whole eggs and egg whites, one at a time, followed by the vanilla and sour cream.
2 large whole eggs, 2 large egg whites, 2 tsp vanilla extract, 1/4 cup (60g) sour cream
Stir in half of the flour mixture and mix in the milk.
3/4 cup (190ml) milk
Then stir in the remaining flour mixture until just combined. Pour the batter into the prepared pan.
Bake for 25-30 minutes or until an inserted toothpick comes out clean. Allow the cake to cool fully before frosting.
Frosting
Beat the butter, salt, and vanilla until light and fluffy.
1 cup (227g) unsalted butter, seeds of 1 vanilla bean, 1/4 tsp salt
Add in the powdered sugar, 1 cup at a time, mixing well in between. Add in the cream or milk, 1 tablespoon at a time as needed.
4 cups (500g) powdered sugar, 4-6 Tbsp milk or cream
Beat on high speed for about 1 minute after the last addition of powdered sugar for a fluffy and airy texture. Spread on cooled cake and decorate with sprinkles if desired.
sprinkles for decorating
Notes
Leftover cake can be covered and stored in the refrigerator for up to 5 days. Bring to room temperature by letting it sit out on the counter for 1 hour before serving.