Preheat your oven to 160°C (325°F). Lightly grease a loaf pan approximately 11x6x3 inches and line it with parchment paper for easy removal.
In a large bowl, add the eggs and sugar. Beat until well combined and the mixture becomes slightly foamy.
3 eggs, 1 cup sugar
Add the lemon zest, vanilla extract, and olive oil to the bowl. Continue beating until all ingredients are fully incorporated. Whisk in the natural yogurt and lemon juice to the bowl and mix well until all liquid ingredients are evenly combined.
1 cup natural yogurt, ⅓ cup olive oil, 1 tablespoon vanilla extract, 1 tablespoon lemon zest, 3 tablespoons lemon juice
In another bowl, sift the flour and baking powder together to ensure there are no lumps.
2 cups all-purpose flour, 1 tablespoon baking powder
Gradually add the sifted dry ingredients to the liquid mixture, gently folding with a spatula until the batter is smooth and there are no flour clumps.
Pour the batter into the prepared pan, ensuring it is evenly distributed. Bake in the preheated oven for approximately 35-40 minutes, or until the top of the loaf is golden brown and a toothpick inserted into the center comes out clean.
While the loaf cools in the pan for a few minutes, prepare the lemon glaze by mixing the powdered sugar with lemon juice until smooth and pourable.
1 cup powdered sugar, 1 tablespoon lemon juice
Remove the loaf from the pan and place it on a wire rack to cool completely. Once cooled, pour the lemon glaze over the top of the loaf.
Slice into portions and serve.