Arrange the oven shelf to the middle position. Preheat oven to 350ºF (177ºC). Butter and flour 2-9 inch diameter cake pans.
In the bowl of a stand-up mixer, add sugar (2 1/4 cups) and orange zest (1/4 cup). Set mixer, set on medium, beat until mixture is very fragrant, about 2 minutes; set aside.
In a medium mixing bowl, whisk together flour (3 1/3 cups), salt (1 teaspoon), baking powder (2 1/4 teaspoons), and baking soda (3/4 teaspoon); set aside.
In the bowl of a stand mixer, beat the oil (1 1/3 cups) and sugar/zest mixture until light and fluffy, 4-6 minutes.
Add eggs (4), one at a time, beating just until the yolk disappears and is incorporated into the batter.
With the mixer set on low, add orange juice (1 1/3 cups) and flour mixture, alternating, beginning and ending with flour. Stir in vanilla extract (2 teaspoons).
Pour batter evenly into prepared pans. Place in staggered positions on middle oven shelf and bake 20 minutes, rotate pans, then loosely tent pans. Continue to bake 10-15 minutes more, or until a toothpick inserted in center comes out clean.