Preheat the oven to 180°C (350°F). Grease and flour a 22 cm (9 inch) round cake pan.
In a medium bowl, sift together the all-purpose flour, baking powder, and salt. Set aside.
In a large mixing bowl, whisk the eggs and granulated sugar together until pale and fluffy, about 3-4 minutes.
Slowly add the extra virgin olive oil to the egg mixture while whisking continuously until fully incorporated.
Add the whole milk, fresh lemon juice, lemon zest, and vanilla extract to the wet mixture and whisk until combined.
Gradually fold the dry ingredients into the wet ingredients using a spatula 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 to a wire rack to cool completely.
Once cooled, dust the top of the cake with powdered sugar before serving.