Preheat the oven to 325 degrees F. Grease and flour a bundt pan or tube pan. (We used a 15 cup pan with a baking capacity of 12 cups.) See notes.
Go ahead and separate your eggs, saving only the 6 egg whites needed for this recipe. Set them in a bowl to the side. (If using carton egg whites instead, pour the appropriate amount of egg whites into measuring cup and set aside.)
In a medium bowl, whisk the flour, baking powder, baking soda, and salt for 30 seconds and set aside.
In another bowl, add the buttermilk, vegetable oil, and vanilla extract and peppermint extract. Set aside.
In the bowl of your mixer, add the butter and cream cheese and mix at medium speed until smooth.
Gradually add the sugar and mix at medium speed for 2-3 minutes.
Mixing on low speed, add the 6 egg whites one at a time (it's fine to estimate), mixing 3-5 seconds to incorporate after each addition.
With the mixer on low speed, alternately add the flour mixture and the buttermilk mixture, beginning and ending with the flour mixture (We did 3 additions of the dry mixture, 2 additions of wet).
Mix the batter just until well combined- be careful not to over-mix.
Reserve 1 ½ cups of batter and place in a small bowl. Tint this batter red.