Preheat the oven to 350°F. Prepare three 7-inch round cake pans with nonstick cooking spray and parchment paper circles.
In a mixing bowl, whisk together the all-purpose flour, baking powder, and salt. Set aside.
In the bowl of a stand mixer fitted with a paddle attachment or in a large bowl with an electric hand mixer, cream the granulated sugar, unsalted butter, and vegetable oil until smooth and creamy. Add the eggs, egg yolks, and vanilla extract and mix until smooth.
Alternate adding the dry ingredients with the buttermilk, starting and ending with the dry ingredients, and mixing in between each addition. (Add ⅓ flour mixture, ½ buttermilk, ⅓ flour mixture, ½ buttermilk, ⅓ flour mixture). Scrape the sides and bottom of the bowl and mix the batter until it is smooth.
Divide the cake batter evenly into the prepared cake pans. Bake the cake layers for approximately 28 to 30 minutes, until the tops of the cakes bounce back when gently touched. Remove the cake pans from the oven and cool the cake layers for 15 minutes. Remove the cake layers from the pan and transfer to a wire rack to cool completely.