Preheat oven to 350 degrees. Grease two 9-inch-wide by 2-inch-high round cake pans and line bottoms with parchment paper. Dust with flour.
Whisk flour, baking powder, baking soda, salt, and 1 1/2 cups sugar together in large bowl.
Whisk melted butter, buttermilk, oil, vanilla, and yolks in another bowl (or a 4 cup liquid measure).
Using a stand mixer with whisk attachments, beat egg whites until foamy. Gradually add remaining 1/4 cup sugar and beat until stiff peaks form. Transfer to a separate bowl so that your mixing bowl is clean.
Add flour mixture to the empty mixing bowl. With whisk still attached and with mixer at low speed, gradually pour in butter mixture and mix until almost incorporated (a few streaks of dry flour will remain), about 15 seconds. Stop mixer and scrape whisk and sides of bowl. Return mixer to medium-low speed and beat until smooth and fully incorporated, 10 to 15 seconds.
Using rubber spatula, stir 1/3 of whites into batter to lighten, then add remaining whites and gently fold into batter until no white streaks remain. Divide batter evenly between prepared cake pans. Lightly tap pans against counter 2 or 3 times to dislodge any large air bubbles.
Bake for 20 to 22 minutes or until cakes appear set and are beginning to pull away from sides of pan. Let cakes cool on wire rack for 10 minutes. Loosen cakes and invert.