Preheat the oven to 180°C (350°F). Grease and flour a 22 cm (9-inch) round cake pan.
In a medium bowl, whisk together the all-purpose flour, baking powder, and salt. Set aside.
In a large bowl, beat the eggs and granulated sugar with an electric mixer on medium speed until pale and fluffy, about 3-4 minutes.
Add the extra virgin olive oil, whole milk, lemon zest, lemon juice, and vanilla extract to the egg mixture. Mix until well combined.
Gradually fold the dry ingredients into the wet ingredients using a spatula, mixing gently until just combined. Do not overmix.
Pour the batter into the prepared cake pan and smooth the top with a spatula.
Bake in the preheated oven for 35-40 minutes, or until a toothpick inserted into the center comes out clean.
Remove the cake from the oven and allow it to cool in the pan for 10 minutes. Then transfer it to a wire rack to cool completely.
Once cooled, dust the top of the cake with powdered sugar before serving.