Preheat your oven to 350°F (175°C). Grease the 9-inch round cake pan and line the bottom with parchment paper.
In a large mixing bowl, combine the granulated sugar and lemon zest. Use your fingers to rub the zest into the sugar until fragrant.
Add the eggs, olive oil, and milk to the sugar mixture. Whisk until well combined.
In a separate bowl, sift together the flour, baking powder, and salt. Gradually add the dry ingredients to the wet mixture, stirring gently until just combined.
Fold in the freshly squeezed lemon juice until incorporated.
Pour the batter into the prepared cake pan and smooth the top with a rubber spatula.
Bake in the preheated oven for 30 minutes, or until a toothpick inserted into the center comes out clean.
Allow the cake to cool in the pan for about 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.