Preheat oven to 160 degrees C (320 degrees F). Lightly grease a 11x6x3 inches loaf pan and line with parchment paper, generously (it's easiest to lift the cooked cake out of the tin with the paper).

In a large mixing bowl, beat the eggs and sugar until well combined and the mixture starts to become foamy.

Add the lemon zest, vanilla extract, and olive oil to the bowl. Continue beating until thoroughly incorporated.

Add the natural yogurt and lemon juice to the bowl and mix well until all liquid ingredients are evenly combined.

Now, place a seive over the mixing bowl and sift in the dry ingredients (flour and baking powder). You want to ensure there are no lumps in the flour mixture for the cake batter.

Now gently fold the flour through the batter with a spatula until smooth and no flour clumps remain.

Pour the olive oil yogurt cake batter into the lined loaf tin.

Bake in the preheated oven for 35-40 minutes, or until the top of the loaf is golden brown and cooked through.

Check with the toothpick text (when inserted into the center of the cake the toothpick should come out clean).

While the baked cake cools in the loaf tin for a few minutes, prepare the lemon glaze.

Mix the powdered sugar with the lemon juice in a medium bowl until smooth and easy to pour.

Remove the loaf from the pan and place it on a wire rack to cool down fully. Once cool, pour the lemon glaze over the top.

Slice the cake into portions and serve.