Preheat oven to 325 degrees Fahrenheit.
Grease and flour two 8" round (2" inch deep) cake pans and set aside.
Add one cup of milk to a measuring cup and add in one tablespoon of lemon juice. Stir and set aside.
In a large mixing bowl, whisk together the flour, sugar, baking soda, baking powder and salt.
In another bowl, add the milk & lemon juice mixture, another ½ cup of milk, the vinegar, oil, food coloring, princess emulsion (or extract) and egg whites. Whisk well and set aside.
Make sure your butter is at room temperature. Add the butter (in chunks) slowly to your dry ingredients. (You can turn your stand mixer on low and leave it on while you add the butter chunks at a time, or you can use a hand mixer.)
Turn the mixer up to medium and mix until all the flour is coated with the butter and the mixture is crumbly. It will have a sand-like texture.
Pour in about a third of the liquid mixture. Mix on low to medium until just combined. About 15-20 seconds.
Pour the last of the liquid mixture and mix again until combined. Don't over mix the batter. Mixing it for several minutes is too long. Once all the ingredients are incorporated well, stop mixing.
Use a rubber spatula and scrape the sides and bottom of the bowl. Mix again for only about 10 to 15 seconds.
Check the color, if it needs to be more pink, add in another drop or two of the gel food coloring. (The batter will need to be a bit brighter than you want the baked cake to be, since the cake will darken a bit and become more golden and may over power a super light pink color.)
Mix until the food coloring is well incorporated, but be careful not to mix too long here, or it will affect your cake's texture.
Pour into prepared pans and bake at 325 degrees for approximately 45 minutes. A toothpick inserted should come out with some crumbs on it.
Set on wire racks to cool for 10-15 minutes, then turn the cakes out onto the racks and let them cool out of the pans completely before adding frosting.
Once cooled, add buttercream.