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 plain milk, the vinegar, oil, food coloring, princess emulsion (or extracts) and egg whites. Whisk well and set aside.
Make sure the butter is almost room temperature, but not very warm. Add the butter (in chunks) slowly to the dry ingredients. If using a stand mixer, just turn the mixer on low and leave it on while the butter chunks are added a bit at a time, or just use a hand mixer.
Once all the butter has been added, turn the mixer up to medium-high and mix until all the flour is coated with the butter and the mixture is crumbly. It will have a sand-like texture. Stop mixing once the flour is all coated. Mixing too long will form the mixture into a paste.
Pour about a third of the liquid mixture into the flour and butter mixture. Mix on medium until just combined. About 15-20 seconds.
Pour the last of the liquid mixture in and mix again until well combined. Be careful not to overmix. Mixing the batter 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 pinker, 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 become more golden brown and may overpower a subtle 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 the batter into the prepared pans and bake at 325 degrees F for approximately 45-55 minutes. A toothpick inserted into the middle of each layer should come out with a few moist crumbs on it or clean. The cake layers will flatten a bit once cooled.
Set the baked cake layers 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 frosting.