Preheat the oven to 350°F with a rack in the center. Lightly grease an 8" round pan and line the bottom with a parchment round.
In a medium bowl, whisk together the flour, sugar, baking powder, baking soda, and salt.
In a large mixing bowl, vigorously whisk the eggs and olive oil until emulsified; the mixture should look creamy and yellow.
Whisk in the milk, orange zest, orange juice, and vanilla.
While whisking, gradually add the dry ingredients to the wet; continue to whisk until well combined and no lumps remain.
Pour the batter into the prepared pan and bake for 35 to 40 minutes, until the cake is golden brown on top and springs back when gently pressed.
Remove the cake from the oven and transfer it to a wire rack; allow the cake to cool in the pan for 30 minutes.
Run an offset spatula around the edge of the cake, turn the cake out onto the rack, and allow it to cool completely.
Cut into slices and serve with a dusting of confectioners’ sugar, a large dollop of whipped cream and berries, or on its own.
Store any leftover olive oil cake well-wrapped at room temperature for up to 4 days. The cake will become moister and more flavorful as it sits.
