Using a mixer, cream the 2/3 cup unsalted butter, softened, 1 cup granulated sugar and 1 cup dark brown sugar, until light, around 3 minutes.
Add 3 large eggs, one at time.
Add in the dry ingredients alternately with the 1 1/4 cups buttermilk, in three separate batches, beginning and ending with the dry ingredients.
Pour into prepared cake pans. Bake at 350° F for 30-35 minutes, or until a toothpick inserted in the center comes out clean. Cool cakes in pans 15-20 minutes before carefully removing from cake pans and allowing to cool completely on a wire rack before frosting.
For the frosting
In a double boiler, bring 1 1/4 cups dark brown sugar,1/4 teaspoon cream of tartar, pinch of salt, 1/3 cup water and 1 Tablespoon light corn syrup to a boil.
Cook until the sugar dissolves (test by rubbing a small amount between your fingers; it should not feel grainy).
Place the 2 large egg whites, room temperature, in a large mixing bowl or the bowl of a stand mixer; slowly pour in hot sugar mixture.
Using mixer, beat on high until of spreading consistency, around 6-7 minutes.
Add 1/2 teaspoon vanilla extract in last; frost cake immediately.
Notes
The frosting is best eaten the day it is made; store leftovers up to 3 days (frosting will form a crust)
Cake layers can be made in advance if sealed well; refrigerate up to 3 days or freeze up to 45 . If freezing, thaw cake layers in refrigerator before frosting.
Pasteurized egg white product (in a carton) does not work well for this recipe.