Preheat oven to 350 degrees. Line the bottom of 3 8-inch cake pans then spray it with baking non-stick spray.
In the bowl of a stand-up mixer, combine the butter, 1 3/4 cup of sugar, and the vanilla, using medium speed for 5 minutes, scraping down the bowl, until the mixture is light and fluffy. Mix in the egg yolks, one at a time, mixing just until the yellow disappears, before adding the next.
In another mixing bowl, whisk together flour, salt, baking powder and baking soda. Turn the stand-up mixer on low, and alternate adding the flour mixture then the sour cream, to the butter mixture, one-third of each at a time, allowing them to just incorporate before adding the next. When finished with adding both, turn the mixer on medium speed and mix for 2 minutes.
Pour the batter into a clean mixing bowl. Wash and dry the bowl of the stand-up mixer and fit with the whisk attachment. Add the egg whites and beat on medium speed for 5 minutes until opaque white and foamy. Add the remaining 1/4 sugar and continue to beat on medium until soft peaks form. Gently fold into batter in 3 additions.
Scrape the batter evenly into the prepared cake pans. Bake in preheat ovens, rotating pans halfway through, until they are lightly golden and a toothpick inserted in the center of the cake comes out clean, about 30-35 minutes.
Allow cakes to cool, in pans, set on a wire baking rack for 10 minutes. Remove cakes from pans and cool completely on wire rack, about 3 hours.
When Cooled, brush tops and sides of each cake layer with about 2 tablespoons simple syrup per layer.