Preheat oven to 325 degrees. Line sheet pan with parchment paper and spray well with nonstick cooking spray and set aside.
In a large bowl, whisk flour, baking powder, baking soda and salt together to combine. Set aside.
In a liquid measuring cup, stir milk and vanilla together. Set aside.
In a separate large bowl, mix butter, oil and sugar together until combined. Mix in eggs and egg whites, one at a time, until mixture becomes very light and fluffy. Scrape the sides of the bowl and mix again briefly.
Alternate adding in flour mixture with milk mixture, being sure to start and end with flour. Scrape the sides and mix again to ensure a smooth batter.
Pour into prepared sheet pan and smooth the top. Bake 15 minutes in the lower 2/3rds of the oven. Cake will be done when a toothpick comes out clean or mostly clean with a few moist crumbs. Depending on your oven, this will take more or less time. Anywhere between 12-20 minutes.
Cool completely before frosting.