Preheat the oven to 350°F and set an oven rack in the middle position. Butter and flour, or use nonstick cooking spray with flour, such as Baker's Joy, a 9x13-inch ceramic baking pan, or metal pan. Sift together the flour and baking powder to remove any lumps in a large bowl. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, combine the unsalted butter, sugars, oil, pure vanilla, clear vanilla, and salt. On medium speed, beat until light and fluffy for about 5 minutes, stop and scrape the bowl, and paddle with a rubber spatula as necessary.
Add the eggs, beat on medium speed until well combined, about 2 to 3 minutes, and scrape the bowl. On low speed, stream in half of the buttermilk. Increase speed to medium-high and mix for about 1 minute. Scrape the bowl. Add half of the flour mixture and mix on low speed just until combined.
Scrape the bowl again, add the remaining flour mixture and remaining buttermilk and mix just until the batter comes together, about 45 seconds to 1 minute. Finish folding the ingredients by hand using a rubber spatula to ensure the batter is well mixed and smooth; there should be no streaks of fat or liquid.
Evenly pour batter into the prepared pan. Bake Yellow Sheet Cake for 35 to 40 minutes, or until a toothpick inserted in the center comes out clean. Remove the yellow sheet cake from the oven and let it cool in the pan on a wire rack until completely cool.