Preheat oven to 350°F. Butter two 8-inch cake pans and line with buttered parchment.
Whisk the flours, baking powder and salt together in a bowl.
In a stand mixer, fitted with a paddle attachment, cream the butter and sugar together on medium speed for about 5 minutes. Scrape down the bowl. On low-speed slowly add the oil and vanilla until combined. Mix in the yolks and whole eggs one at a time, scrape down the bowl after each. Add the flour in three parts, alternating with the buttermilk, starting and ending with the flour.
In a separate bowl whip the heavy cream to medium peaks. Fold the cream into the cake batter. Divide the batter equally into the cake pans.
Bake for about 35 to 40 minutes or until a tester comes out clean. Allow to cool on a rack.