Preheat the oven to 350°F and grease a 9-inch round cake pan. Line the bottom with parchment paper.

In a medium bowl, whisk together the flour, baking powder, salt, and baking soda.

In a large bowl, place the lemon zest and sugar. Use your fingers to work the zest into the sugar until well combined. This helps the zest release its fragrant oils. Add the olive oil, eggs, lemon juice, milk, and vanilla and whisk until well combined.

Add the dry ingredients to the wet ingredients and whisk until just combined.

Transfer the batter to the prepared pan and smooth the top. Lightly tap the pan on the counter to release any air bubbles. Bake for 40 to 50 minutes, or until the top springs back to the touch and a toothpick inserted comes out clean.

Let cool in the pan for 15 minutes before turning out and transferring to a wire rack to cool completely.