Preheat the oven to 350 degrees F.
Grease three 7 or 8 inch cake pans with butter and coat with flour.
In the bowl of a stand mixer, cream together butter, oil, and sugar.
Add in eggs, vanilla, and yogurt.
Beat until lighter in color and fluffy, about 2-3 minutes.
After you mill your flour, pour it through a sifter and sift until most of the bran is left behind (you should have 2 ½ cups after the flour is sifted).
In a separate bowl, mix together the dry ingredients - flour, baking powder, baking soda, and salt.
Working in batches, add ⅓ of the flour mixture into the wet ingredients, then half of the buttermilk, mixing well, on low speed, between each addition. Repeat, and end with adding in the remaining flour.
Evenly pour batter into the 3 pans.
Bake for 23-28 minutes, until a toothpick inserted in the middle comes out clean.
While the cakes are baking, prepare the icing.
Using the whisk attachment, beat the butter until it is creamed.
Add in half of the powdered sugar, along with the vanilla and half of the milk.
Add in the rest of the powdered sugar and beat on medium-high speed until fluffy.
Add in remaining milk if needed to reach desired consistency.
Allow the cakes to rest 10 minutes before removing from pan.
Let them cool completely, then ice as desired.