Preheat oven to 350°F. Lightly grease a 9-inch round cake pan or springform pan and line the bottom with parchment paper.
In a medium bowl, whisk together flour, baking powder, baking soda, and salt.
In a large mixing bowl, whisk the eggs and sugar until pale yellow and slightly thickened, about 1 minute.
Add olive oil, milk, lemon juice, lemon zest, and vanilla. Whisk until smooth.
Add dry ingredients to the wet mixture and stir just until combined. Do not overmix.
Pour batter into prepared pan. Tap the pan gently on the counter to release any air bubbles.
Bake for 40–45 minutes, or until the top is golden and a toothpick inserted in the center comes out clean.
Cool in the pan for 10 minutes, then transfer to a wire rack. Cool completely before glazing or dusting with powdered sugar.