Preheat the oven to 350º and line a loaf pan with parchment paper.
In a large mixing bowl, combine the lemon zest with the cane sugar by rubbing together with your fingers until the lemon zest is well distributed and you can smell the lemon oils.
Add in the eggs, oil, milk, and vanilla extract. Whisk until fully combined.
To the bowl, add the greek yogurt, then whisk again to incorporate the yogurt.
Add the baking powder and flour to the same bowl, then fold gently with a spatula until the flour is just combined. It is okay if there are some lumps.
Pour the batter into the lined loaf pan, then bake for 55-60 minutes or until fully baked. Let cool 15-20 minutes before adding the glaze and slicing.
For the Glaze
In a medium bowl, whisk together the confectioner's sugar and lemon juice until it makes a thick lemon glaze. Pour directly on top of the lemon loaf and let set for 10 minutes before slicing.
Notes
Do NOT Over Mix - Over mixing this batter (really, any batter) will cause the baked results to be overworked, chewy, gummy, and not very airy. Switch to using a spatula when it comes time to fold in the flour and the other dry ingredients. It will help!Marry the Zest and Sugar - Take your fingertips and rub (yes, rub) the lemon zest with the sugar. This helps to bring out all those luscious lemony oils from the zest and gives the entire loaf a robust lemon flavor. Plus, it smells really really good.